In combinatorics, we work with several key formulas like linear permutations, combinations, and variations. These formulas help in determining the number of possible arrangements, selections, or groupings from a set of objects. Below is an explanation of how each formula is used and their respective notations:<\/p>\n\n\n\n
1. Linear Permutation<\/strong> (also known as Permutation<\/strong>)<\/h3>\n\n\n\n\n- Formula<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: A linear permutation represents the number of ways to arrange r<\/strong> objects from a set of n<\/strong> distinct objects, where the order matters. The formula takes into account the possible arrangements by dividing the total number of possible objects’ factorials by the factorial of the remaining objects not chosen.<\/li>\n\n\n\n
- Example<\/strong>: If you have 5 books and want to know how many ways you can arrange 3 of them, you use: P(5,3)=5!(5\u22123)!=5\u00d74\u00d73!2!=60P(5, 3) = \\frac{5!}{(5-3)!} = \\frac{5 \\times 4 \\times 3!}{2!} = 60P(5,3)=(5\u22123)!5!\u200b=2!5\u00d74\u00d73!\u200b=60<\/li>\n<\/ul>\n\n\n\n
2. Combinations<\/strong> (also known as nCr<\/strong>, Combination<\/strong>)<\/h3>\n\n\n\n\n- Formula<\/strong>: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: Combinations calculate the number of ways to choose r<\/strong> objects from a set of n<\/strong> objects, where the order does not matter. Unlike permutations, the order of selection does not affect the outcome, so we divide by the factorial of the number of selections.<\/li>\n\n\n\n
- Example<\/strong>: If you want to select 3 books from a set of 5, regardless of order, the calculation is: C(5,3)=5!3!(5\u22123)!=5\u00d74\u00d73!3!\u00d72!=10C(5, 3) = \\frac{5!}{3!(5 – 3)!} = \\frac{5 \\times 4 \\times 3!}{3! \\times 2!} = 10C(5,3)=3!(5\u22123)!5!\u200b=3!\u00d72!5\u00d74\u00d73!\u200b=10<\/li>\n<\/ul>\n\n\n\n
3. nPr<\/strong> (Permutation of n<\/strong> objects taken r<\/strong> at a time)<\/h3>\n\n\n\n\n- Formula<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: This is just another way of representing the permutation formula where the number of arrangements of r<\/strong> objects taken from n<\/strong> objects is calculated. This is identical to the linear permutation formula.<\/li>\n<\/ul>\n\n\n\n
4. rCn<\/strong> (Combination of r<\/strong> objects chosen from a set of n<\/strong>)<\/h3>\n\n\n\n\n- Formula<\/strong>: This is the same as the combination formula: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: It denotes the number of ways to choose r<\/strong> objects from n<\/strong>, which is typically referred to as nCr<\/strong> in combinatorics.<\/li>\n<\/ul>\n\n\n\n
Summary:<\/h3>\n\n\n\n\n- Linear permutation<\/strong> is used when order matters<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Combinations<\/strong> are used when order does not matter<\/strong>: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n<\/ul>\n\n\n\n
Each of these formulas has real-world applications like selecting teams, arranging items, or scheduling events.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1170.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"A formula to be used in Linear Permutation * nCr nPr rCn pRc The Correct Answer and Explanation is: In combinatorics, we work with several key formulas like linear permutations, combinations, and variations. These formulas help in determining the number of possible arrangements, selections, or groupings from a set of objects. Below is an explanation […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-261635","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=261635"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
2. Combinations<\/strong> (also known as nCr<\/strong>, Combination<\/strong>)<\/h3>\n\n\n\n\n- Formula<\/strong>: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: Combinations calculate the number of ways to choose r<\/strong> objects from a set of n<\/strong> objects, where the order does not matter. Unlike permutations, the order of selection does not affect the outcome, so we divide by the factorial of the number of selections.<\/li>\n\n\n\n
- Example<\/strong>: If you want to select 3 books from a set of 5, regardless of order, the calculation is: C(5,3)=5!3!(5\u22123)!=5\u00d74\u00d73!3!\u00d72!=10C(5, 3) = \\frac{5!}{3!(5 – 3)!} = \\frac{5 \\times 4 \\times 3!}{3! \\times 2!} = 10C(5,3)=3!(5\u22123)!5!\u200b=3!\u00d72!5\u00d74\u00d73!\u200b=10<\/li>\n<\/ul>\n\n\n\n
3. nPr<\/strong> (Permutation of n<\/strong> objects taken r<\/strong> at a time)<\/h3>\n\n\n\n\n- Formula<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: This is just another way of representing the permutation formula where the number of arrangements of r<\/strong> objects taken from n<\/strong> objects is calculated. This is identical to the linear permutation formula.<\/li>\n<\/ul>\n\n\n\n
4. rCn<\/strong> (Combination of r<\/strong> objects chosen from a set of n<\/strong>)<\/h3>\n\n\n\n\n- Formula<\/strong>: This is the same as the combination formula: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: It denotes the number of ways to choose r<\/strong> objects from n<\/strong>, which is typically referred to as nCr<\/strong> in combinatorics.<\/li>\n<\/ul>\n\n\n\n
Summary:<\/h3>\n\n\n\n\n- Linear permutation<\/strong> is used when order matters<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Combinations<\/strong> are used when order does not matter<\/strong>: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n<\/ul>\n\n\n\n
Each of these formulas has real-world applications like selecting teams, arranging items, or scheduling events.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"A formula to be used in Linear Permutation * nCr nPr rCn pRc The Correct Answer and Explanation is: In combinatorics, we work with several key formulas like linear permutations, combinations, and variations. These formulas help in determining the number of possible arrangements, selections, or groupings from a set of objects. Below is an explanation […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-261635","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=261635"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
3. nPr<\/strong> (Permutation of n<\/strong> objects taken r<\/strong> at a time)<\/h3>\n\n\n\n\n- Formula<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: This is just another way of representing the permutation formula where the number of arrangements of r<\/strong> objects taken from n<\/strong> objects is calculated. This is identical to the linear permutation formula.<\/li>\n<\/ul>\n\n\n\n
4. rCn<\/strong> (Combination of r<\/strong> objects chosen from a set of n<\/strong>)<\/h3>\n\n\n\n\n- Formula<\/strong>: This is the same as the combination formula: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: It denotes the number of ways to choose r<\/strong> objects from n<\/strong>, which is typically referred to as nCr<\/strong> in combinatorics.<\/li>\n<\/ul>\n\n\n\n
Summary:<\/h3>\n\n\n\n\n- Linear permutation<\/strong> is used when order matters<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Combinations<\/strong> are used when order does not matter<\/strong>: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n<\/ul>\n\n\n\n
Each of these formulas has real-world applications like selecting teams, arranging items, or scheduling events.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"A formula to be used in Linear Permutation * nCr nPr rCn pRc The Correct Answer and Explanation is: In combinatorics, we work with several key formulas like linear permutations, combinations, and variations. These formulas help in determining the number of possible arrangements, selections, or groupings from a set of objects. Below is an explanation […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-261635","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=261635"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
4. rCn<\/strong> (Combination of r<\/strong> objects chosen from a set of n<\/strong>)<\/h3>\n\n\n\n\n- Formula<\/strong>: This is the same as the combination formula: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Explanation<\/strong>: It denotes the number of ways to choose r<\/strong> objects from n<\/strong>, which is typically referred to as nCr<\/strong> in combinatorics.<\/li>\n<\/ul>\n\n\n\n
Summary:<\/h3>\n\n\n\n\n- Linear permutation<\/strong> is used when order matters<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Combinations<\/strong> are used when order does not matter<\/strong>: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n<\/ul>\n\n\n\n
Each of these formulas has real-world applications like selecting teams, arranging items, or scheduling events.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"A formula to be used in Linear Permutation * nCr nPr rCn pRc The Correct Answer and Explanation is: In combinatorics, we work with several key formulas like linear permutations, combinations, and variations. These formulas help in determining the number of possible arrangements, selections, or groupings from a set of objects. Below is an explanation […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-261635","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=261635"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Summary:<\/h3>\n\n\n\n\n- Linear permutation<\/strong> is used when order matters<\/strong>: P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n – r)!}P(n,r)=(n\u2212r)!n!\u200b<\/li>\n\n\n\n
- Combinations<\/strong> are used when order does not matter<\/strong>: C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n – r)!}C(n,r)=r!(n\u2212r)!n!\u200b<\/li>\n<\/ul>\n\n\n\n
Each of these formulas has real-world applications like selecting teams, arranging items, or scheduling events.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"A formula to be used in Linear Permutation * nCr nPr rCn pRc The Correct Answer and Explanation is: In combinatorics, we work with several key formulas like linear permutations, combinations, and variations. These formulas help in determining the number of possible arrangements, selections, or groupings from a set of objects. Below is an explanation […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-261635","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=261635"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Each of these formulas has real-world applications like selecting teams, arranging items, or scheduling events.<\/p>\n\n\n\n A formula to be used in Linear Permutation * nCr nPr rCn pRc The Correct Answer and Explanation is: In combinatorics, we work with several key formulas like linear permutations, combinations, and variations. These formulas help in determining the number of possible arrangements, selections, or groupings from a set of objects. Below is an explanation […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-261635","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=261635"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261635\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261635"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261635"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/figure>\n","protected":false},"excerpt":{"rendered":"