{"id":264499,"date":"2025-07-21T13:34:00","date_gmt":"2025-07-21T13:34:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=264499"},"modified":"2025-07-21T13:34:04","modified_gmt":"2025-07-21T13:34:04","slug":"how-many-different-ways-are-there-to-arrange-10-people-in-a-row-of-10-chairs","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/how-many-different-ways-are-there-to-arrange-10-people-in-a-row-of-10-chairs\/","title":{"rendered":"How many different ways are there to arrange 10 people in a row of 10 chairs"},"content":{"rendered":"\n

How many different ways are there to arrange 10 people in a row of 10 chairs?<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The number of different ways to arrange 10 people in a row of 10 chairs is given by the total number of permutations of the 10 individuals. This is a simple case of finding the factorial of 10, written as 10!10!.<\/p>\n\n\n\n

The factorial of a number is the product of all positive integers from 1 to that number. In this case, the factorial of 10 is: 10!=10\u00d79\u00d78\u00d77\u00d76\u00d75\u00d74\u00d73\u00d72\u00d71=3,628,80010! = 10 \\times 9 \\times 8 \\times 7 \\times 6 \\times 5 \\times 4 \\times 3 \\times 2 \\times 1 = 3,628,800<\/p>\n\n\n\n

Therefore, there are 3,628,800<\/strong> different ways to arrange 10 people in a row of 10 chairs.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To understand this, let’s break it down step by step:<\/p>\n\n\n\n

    \n
  1. First Chair:<\/strong> There are 10 people available, so for the first chair, there are 10 possible choices of who can sit in it.<\/li>\n\n\n\n
  2. Second Chair:<\/strong> After the first person is seated, only 9 people remain. Thus, there are 9 choices for who can sit in the second chair.<\/li>\n\n\n\n
  3. Third Chair:<\/strong> Now, with 2 people already seated, only 8 people remain. Therefore, there are 8 choices for the third chair.<\/li>\n<\/ol>\n\n\n\n

    This pattern continues until all the chairs are filled. The total number of ways to arrange the 10 people is the product of these choices: 10\u00d79\u00d78\u00d77\u00d76\u00d75\u00d74\u00d73\u00d72\u00d71=3,628,80010 \\times 9 \\times 8 \\times 7 \\times 6 \\times 5 \\times 4 \\times 3 \\times 2 \\times 1 = 3,628,800<\/p>\n\n\n\n

    This product is also known as 10 factorial (10!)<\/strong>. Factorials are used in permutations and combinations to count possible arrangements when the order matters.<\/p>\n\n\n\n

    Thus, the number of different ways to arrange the 10 people in 10 chairs is 3,628,800<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    How many different ways are there to arrange 10 people in a row of 10 chairs? The correct answer and explanation is: The number of different ways to arrange 10 people in a row of 10 chairs is given by the total number of permutations of the 10 individuals. This is a simple case 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-264499","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264499","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=264499"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264499\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=264499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=264499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=264499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}