{"id":222901,"date":"2025-06-01T05:32:20","date_gmt":"2025-06-01T05:32:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222901"},"modified":"2025-06-01T05:32:22","modified_gmt":"2025-06-01T05:32:22","slug":"find-the-number-of-combinations-5c4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/find-the-number-of-combinations-5c4\/","title":{"rendered":"Find the number of combinations: 5C4"},"content":{"rendered":"\n<p>Find the number of combinations: 5C4<br>Find the number of combinations: 5C4<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p>(54)=5\\binom{5}{4} = 5<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation <\/h3>\n\n\n\n<p>The expression <strong>5C4<\/strong>, also written as (54)\\binom{5}{4}, represents the number of <strong>combinations<\/strong> of 5 items taken 4 at a time. In combinatorics, a <strong>combination<\/strong> refers to the selection of items <strong>without regard to the order<\/strong> in which they are selected. This is different from a <strong>permutation<\/strong>, where order <strong>does<\/strong> matter.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Formula for Combinations:<\/strong><\/h4>\n\n\n\n<p>(nr)=n!r!(n\u2212r)!\\binom{n}{r} = \\frac{n!}{r!(n &#8211; r)!}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>nn = total number of items<\/li>\n\n\n\n<li>rr = number of items to choose<\/li>\n\n\n\n<li>n!n! (n factorial) = n\u00d7(n\u22121)\u00d7(n\u22122)\u00d7\u2026\u00d71n \\times (n &#8211; 1) \\times (n &#8211; 2) \\times \\ldots \\times 1<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Applying to 5C4:<\/strong><\/h4>\n\n\n\n<p>(54)=5!4!(5\u22124)!=5!4!\u22c51!\\binom{5}{4} = \\frac{5!}{4!(5 &#8211; 4)!} = \\frac{5!}{4! \\cdot 1!}<\/p>\n\n\n\n<p>Calculating factorials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5!=1205! = 120<\/li>\n\n\n\n<li>4!=244! = 24<\/li>\n\n\n\n<li>1!=11! = 1<\/li>\n<\/ul>\n\n\n\n<p>(54)=12024\u22c51=12024=5\\binom{5}{4} = \\frac{120}{24 \\cdot 1} = \\frac{120}{24} = 5<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Interpretation:<\/strong><\/h4>\n\n\n\n<p>Choosing 4 items out of 5 without caring about order gives us 5 unique combinations. This makes intuitive sense. If you have 5 people \u2014 say A, B, C, D, and E \u2014 and you want to select <strong>4 of them<\/strong>, then the number of ways you can do that is equal to the number of different people who could be <strong>left out<\/strong> (since selecting 4 out of 5 is equivalent to <strong>omitting<\/strong> 1 out of 5). You can leave out A, or B, or C, or D, or E \u2014 5 possibilities.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Conclusion:<\/strong><\/h4>\n\n\n\n<p>(54)=5\\boxed{\\binom{5}{4} = 5}<\/p>\n\n\n\n<p>This is a basic but important result in combinatorics, useful in probability, statistics, and many areas of mathematics and computer science.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-10.jpeg\" alt=\"\" class=\"wp-image-222902\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the number of combinations: 5C4Find the number of combinations: 5C4 The Correct Answer and Explanation is: Correct Answer: (54)=5\\binom{5}{4} = 5 Explanation The expression 5C4, also written as (54)\\binom{5}{4}, represents the number of combinations of 5 items taken 4 at a time. In combinatorics, a combination refers to the selection of items without regard [&hellip;]<\/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-222901","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222901","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=222901"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222901\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222901"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222901"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}