{"id":6568,"date":"2014-02-24T17:13:04","date_gmt":"2014-02-24T17:13:04","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6568"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"math-review-of-permutations-and-factorials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-permutations-and-factorials\/","title":{"rendered":"Math Review of Permutations and Factorials"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Permutations and factorials are closely related mathematical concepts.\u00a0 Permutations relate to the order of objects, while factorials involve all possible outcomes of an event.\u00a0 If items are ordered in a particular way, factorials determine the number of times they can be ordered.<\/p>\n

What Are Permutations?<\/strong><\/p>\n

Permutations are rankings where the order matters.\u00a0 Suppose a music producer is choosing the order of songs on a CD released from a new artist.\u00a0\u00a0Only one song can be in each track.\u00a0 If there are 10 songs that have been recorded, there are 10 possibilities for the opening track.\u00a0 Since one song has already been chosen, there are 9 left for the second track.\u00a0 For the third track, there are 8 left, and so on, until the last song remains.\u00a0 The way to calculate the number of permutations is 10 \u2219 9 \u2219 8 \u2219 7 \u2219 6 \u2219 5 \u2219 4 \u2219 3 \u2219 2 \u2219 1\u00a0 = 3, 628, 800.<\/p>\n

What Are Factorials?<\/strong><\/p>\n

Factorials involve all possible outcomes of an event.\u00a0 They are multiplications that start with the number of events multiplied by the number of events -1 and so on, until there is only 1 left.\u00a0 In the example where there were 10 songs on a side of the CD, 10! (read 10 factorial) is 10 \u2219 9 \u2219 8 \u2219 7 \u2219 6 \u2219 5 \u2219 4 \u2219 3 \u2219 2 \u2219 1.\u00a0 The number 0! is equal to 1, much in the same way that x0<\/sup> is equal to 1.\u00a0 It is a mathematical convention that makes calculations easier.<\/p>\n

What Are Combinations?<\/strong><\/p>\n

Combinations are rankings where the order doesn’t matter.\u00a0 For example, suppose 5 people are chosen out of a group of 10 to be on a committee.\u00a0 In this case, it doesn’t matter in what order they are chosen, because the end result is the same.\u00a0 An entire group of people are chosen.\u00a0 If the order mattered, it would be 10 \u2219 9 \u2219 8 \u2219 7 \u2219 6\u00a0 = 30240.\u00a0 Since the order does matter, it will be a subset of the 30240.\u00a0 How many of the groups of 5 contain the same members in whatever order?\u00a0 That can be answered by the factorial 5!, which is 5 \u2219 4 \u2219 3 \u2219 2 \u2219 1 = 120.\u00a0 30240\/120 = 252.<\/p>\n

How Are They Different?<\/strong><\/p>\n

Suppose there are 11 runners in a race.\u00a0 Most of the time, all 11 runners aren’t given places, just the first 3.\u00a0 There are 11 possibilities for first place, 10 possibilities for second place, and 9 possibilities for third place, or 990 permutations in the first 3 places.\u00a0 If all runners were given places, that would lead to 11! places, or 39,916,800 possible combinations.<\/p>\n

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Overview: Permutations and factorials are closely related mathematical concepts.\u00a0 Permutations relate to the order of objects, while factorials involve all possible outcomes of an event.\u00a0 If items are ordered in a particular way, factorials determine the number of times they can be ordered. What Are Permutations? Permutations are rankings where the order matters.\u00a0 Suppose a […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[315,644,1318],"class_list":["post-6568","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-combinations","tag-factorials","tag-permutations"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6568"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6568\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6568"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}