{"id":222790,"date":"2025-05-31T18:31:55","date_gmt":"2025-05-31T18:31:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222790"},"modified":"2025-05-31T18:31:57","modified_gmt":"2025-05-31T18:31:57","slug":"find-the-value-of-the-permutation-4p3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/31\/find-the-value-of-the-permutation-4p3\/","title":{"rendered":"Find the value of the permutation. 4P3"},"content":{"rendered":"\n

Question
Find the value of the permutation. 4P3
Find the value of the permutation<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Answer:<\/strong>
The value of the permutation 4P3<\/strong> is 24<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

A permutation<\/strong> refers to an arrangement of objects in a specific order. The notation nPr<\/strong> represents the number of permutations of r<\/strong> items selected from a total of n<\/strong> distinct items, where order matters<\/strong>.<\/p>\n\n\n\n

The formula to calculate a permutation is: nPr=n!(n\u2212r)!nP_r = \\frac{n!}{(n – r)!}<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n

    \n
  • n!<\/strong> (n factorial) is the product of all positive integers up to n.<\/li>\n\n\n\n
  • (n – r)!<\/strong> is the factorial of the difference between n and r.<\/li>\n<\/ul>\n\n\n\n

    Let\u2019s apply this to 4P3<\/strong>: 4P3=4!(4\u22123)!=4!1!4P_3 = \\frac{4!}{(4 – 3)!} = \\frac{4!}{1!}<\/p>\n\n\n\n

    First, calculate the factorials:<\/p>\n\n\n\n

      \n
    • 4! = 4 \u00d7 3 \u00d7 2 \u00d7 1 = 24<\/li>\n\n\n\n
    • 1! = 1<\/li>\n<\/ul>\n\n\n\n

      So: 4P3=241=244P_3 = \\frac{24}{1} = 24<\/p>\n\n\n\n

      This means there are 24 different ways<\/strong> to arrange 3 items out of a set of 4 when the order of selection matters<\/strong>.<\/p>\n\n\n\n

      \n\n\n\n

      Understanding Through an Example:<\/strong><\/h3>\n\n\n\n

      Suppose you have 4 people: A, B, C, and D. You want to assign 3 of them to 3 different positions: President, Vice President, and Secretary. Since the positions are different, the order<\/strong> in which you assign them matters.<\/p>\n\n\n\n

      Let\u2019s look at a few possibilities:<\/p>\n\n\n\n

        \n
      • A, B, C<\/li>\n\n\n\n
      • A, C, B<\/li>\n\n\n\n
      • B, A, C<\/li>\n\n\n\n
      • B, C, A<\/li>\n\n\n\n
      • C, A, B<\/li>\n\n\n\n
      • C, B, A
        … and many more, totaling 24 unique ordered arrangements<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        If the order did not matter (e.g., combinations), there would be fewer arrangements. But since order does<\/strong> matter in permutations, we count all the possible ways the items can be ordered.<\/p>\n\n\n\n

        Thus, 4P3 = 24<\/strong>, meaning 24 different permutations of 3 items chosen from 4.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        QuestionFind the value of the permutation. 4P3Find the value of the permutation The Correct Answer and Explanation is: Answer:The value of the permutation 4P3 is 24. Explanation A permutation refers to an arrangement of objects in a specific order. The notation nPr represents the number of permutations of r items selected from a total of […]<\/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-222790","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222790","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=222790"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222790\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222790"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222790"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}