{"id":3604,"date":"2021-08-01T09:09:18","date_gmt":"2021-08-01T09:09:18","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3604"},"modified":"2021-11-27T22:11:51","modified_gmt":"2021-11-27T16:41:51","slug":"formula-for-circular-permutation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-circular-permutation\/","title":{"rendered":"What is the Formula for Circular Permutation ?"},"content":{"rendered":"

Here, we will learn circular permutation and the formula for circular permutation with examples.<\/p>\n

Let’s begin –<\/p>\n

Circular Permutation :<\/h2>\n

If there are 4 different things, then for each circular arrangement number of linear arrangement is 4.<\/p>\n

Similarly, if n different things are arranged along a circle, for each circular arrangements number of linear arrangement is n.<\/p>\n

Therefore, the number of linear arrangements of n different things is n \\(\\times\\) (number of circular arrangements of n different things). Hence the number of circular arrangements of n different things is –<\/p>\n

\n

\\(1\\over n\\) \\(\\times\\) (number of linear arrangements of n different things) = \\(n!\\over n\\) = \\((n – 1)!\\)<\/p>\n<\/blockquote>\n

Formula :<\/h2>\n

therefore note that, the formula for circular permutation is –<\/p>\n

(i) The number of circular permutation of n different things taken all at a time is:<\/p>\n

\n

(n – 1)!<\/p>\n<\/blockquote>\n

If the clockwise and anticlockwise circular permutations are considered to be same, then it is:<\/p>\n

\n

\\((n – 1)!\\over 2\\)<\/p>\n<\/blockquote>\n

(ii) Number of circular permutations of n different things taking r at a time distinguishing clockwise and anticlockwise arrangements is :<\/p>\n

\n

\\(^{n}P_r\\over r\\)<\/p>\n<\/blockquote>\n\n\n

Example : <\/span> A person invites a group of friends at dinner. They sit

\n(i) 5 on one round table and 5 on other round table

\n(ii) 4 on one round table and 6 on other round table

\nFind the number of ways in each case in which he can arrange the friends.<\/p>\n

Solution : <\/span>(i) The number of ways of selection of 5 friends for the first table is \\(^{10}C_5\\). Remaining 5 friends are left for the second table.

\nThe total number of permutation of 5 friends at a round table is 4!. Hence, the total number of arrangements is \\(^{10}C_5\\) \\(\\times\\) 4! \\(\\times\\) 4!

\n \t\t (ii) The number of ways of selection of 6 friends is \\(^{10}C_6\\). Remaining 4 friends are left for the second table.

\nThe number of ways of permutation of 6 friends at a round table is 5!. The number of ways of 4 friends at a round table is 3!

\nHence, the total number of arrangements is \\(^{10}C_6\\) \\(\\times\\) 5! \\(\\times\\) 3!

<\/p>\n\n\n

Hope you learnt the formula for circular permutation, learn more concepts of permutation and combination and practice more questions to get ahead in the competition. Good luck!<\/p>\n\n\n

\n
Next – Dearrangement Formula | Permutations of Alike Objects<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Total Number of Combinations<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, we will learn circular permutation and the formula for circular permutation with examples. Let’s begin – Circular Permutation : If there are 4 different things, then for each circular arrangement number of linear arrangement is 4. Similarly, if n different things are arranged along a circle, for each circular arrangements number of linear arrangement …<\/p>\n

What is the Formula for Circular Permutation ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[18],"tags":[538,537,529],"yoast_head":"\nWhat is the Formula for Circular Permutation ?<\/title>\n<meta name=\"description\" content=\"In this post, you will learn circular permutation and what is the formula for circular permutation with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the Formula for Circular Permutation ?\" \/>\n<meta property=\"og:description\" content=\"In this post, you will learn circular permutation and what is the formula for circular permutation with examples.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-01T09:09:18+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-27T16:41:51+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"What is the Formula for Circular Permutation ?\",\"datePublished\":\"2021-08-01T09:09:18+00:00\",\"dateModified\":\"2021-11-27T16:41:51+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/\"},\"wordCount\":369,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"circular permutation\",\"formula for circular permutation\",\"permutation and combination\"],\"articleSection\":[\"Permutation & Combination\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/\",\"url\":\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/\",\"name\":\"What is the Formula for Circular Permutation ?\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-08-01T09:09:18+00:00\",\"dateModified\":\"2021-11-27T16:41:51+00:00\",\"description\":\"In this post, you will learn circular permutation and what is the formula for circular permutation with examples.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-circular-permutation\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"What is the Formula for Circular Permutation ?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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