{"id":7379,"date":"2022-03-21T14:54:23","date_gmt":"2022-03-21T09:24:23","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7379"},"modified":"2022-03-21T14:54:26","modified_gmt":"2022-03-21T09:24:26","slug":"what-is-permutation","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-permutation\/","title":{"rendered":"What is permutation?"},"content":{"rendered":"\n

Permutation<\/strong> <\/a>(Factorial function)-<\/strong> We denote the product of the positive integers from 1 to n by n! and we read it as \u201cfactorial <\/p>\n\n\n\n

It is expressed as below-<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Note-<\/p>\n\n\n\n

Binomial coefficient<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Example: <\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Permutation<\/strong><\/p>\n\n\n\n

We call the arrangement of a set of n objects in a given order- permutation.<\/p>\n\n\n\n

Any arrangement of any of these objects is r-permutation.<\/p>\n\n\n\n

The number of permutations of n objects taken r- P(n, r)<\/p>\n\n\n\n

Formula for P(n, r) is- \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Permutation with repetitions<\/strong><\/h2>\n\n\n\n

The number of permutations of n <\/em>objects of which are alike is, so that we write it as<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Sampling with or without replacement<\/strong><\/p>\n\n\n\n

Suppose we chose the samples with repetition, fro example if we draw a ball from a urn then we put back that ball in the urn and again we pick a ball and we continue the process, so this is the case of sampling with repetition<\/p>\n\n\n\n

Then the product rule tells us that the number of such samples is-<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

And if we pick a ball from the urn and we do not put it back to the urn, then this is the case of sampling without replacement.<\/p>\n\n\n\n

So that in this case the number of samples are-<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Example-<\/strong><\/p>\n\n\n\n

If we choose<\/strong> three cards<\/strong> one after the other from a 52-card deck. Find the number m of ways<\/strong><\/p>\n\n\n\n

This can be done: (a) with replacement; (b) without replacement.<\/strong><\/p>\n\n\n\n

Sol.<\/p>\n\n\n\n

(a) Each card can be chosen in 52 ways. Thus m = 52(52)(52) = 140 608.<\/p>\n\n\n\n

(b) Here there is no replacement. Thus the first card can be chosen in 52 ways, the second in 51 ways, and the third in 50 ways. So that-<\/p>\n\n\n\n

P(52, 3) = 52(51)(50) = 132 600<\/p>\n\n\n\n

Example-<\/strong><\/p>\n\n\n\n

There are 4 black, 3 green and 5 red balls. In how ma<\/strong>ny ways we arrange them in a row?<\/strong><\/p>\n\n\n\n

Solution: <\/strong>Total number of balls = 4 black + 3 green + 5 red = 12<\/p>\n\n\n\n

The black balls are alike,<\/p>\n\n\n\n

The green balls are, and the red balls are alike,<\/p>\n\n\n\n

The number of ways in which we can arrange the balls in a row =<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Circular permutations<\/strong><\/h2>\n\n\n\n

A circular permutation of n <\/em>objects is an arrangement of the objects around a circle.<\/p>\n\n\n\n

If the n <\/em>objects are to be arranged round a circle we take an objects and fix it in one position.<\/p>\n\n\n\n

Now the remaining (n <\/em>\u2013 1) objects can be arranged to fill the (n <\/em>\u2013 1) positions the circle in (n <\/em>\u2013 1)! ways.<\/p>\n\n\n\n

Hence the number of circular permutations of n <\/em>different objects = (n <\/em>\u2013 1)!<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

We denote the product of the positive integers from 1 to n by n! and we read it as \u201cfactorial <\/p>\n","protected":false},"author":28,"featured_media":7397,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-7379","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"\nWhat is permutation? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"We denote the product of the positive integers from 1 to n by n! and we read it as \u201cfactorial\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.goseeko.com\/blog\/what-is-permutation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is permutation? 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