{"id":6982,"date":"2014-05-06T18:03:36","date_gmt":"2014-05-06T18:03:36","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6982"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-factorials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/05\/06\/math-review-of-factorials\/","title":{"rendered":"Math Review of Factorials"},"content":{"rendered":"

Overview:<\/h3>\n

Factorials involve all possible outcomes of an event.\u00a0 They are calculated by multiplying the number of possible events times the number of events minus 1 times the number of events minus 2 until there is only one possibility left.<\/p>\n\n\n\n
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Figure 1:\u00a0 The factorial formula in mathematical symbols<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Example of a Factorial:<\/h3>\n

Suppose four actresses are chosen for a picture:\u00a0 Amy Adams, Charlize Theron, Halle Berry, and Jennifer Lawrence.\u00a0 Obviously, all four cannot have their names first on the billing, but there are four possibilities for the first billing to be chosen.\u00a0 For the second billing, there are only three possibilities, as the first one was chosen.\u00a0 For the third billing, there are only two possibilities, and for the fourth, there is only one.\u00a0 In this case, the multiplication 4\u22193\u22192\u22191 is read as 4! (4 factorial).\u00a0 There are 24 different outcomes for the billing.<\/p>\n\n\n\n
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Figure 2:\u00a0 The factorial 4! Showing 24 different outcomes<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Permutations:<\/h3>\n

Permutations are one of the applications for factorials.\u00a0 They are rankings where the order matters, as in the example of the order of star billing.\u00a0 Suppose a music producer is choosing the order of songs on a CD released from a new artist.\u00a0\u00a0 Only 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\u22199\u22198\u22197\u22196\u22195\u22194\u22193\u22192\u22191 = 3, 628, 800. It would be difficult to list all of those permutations, but not impossible.\u00a0 If there are only 3 events to choose from, there are only 3\u22192\u22191 or 6 possible combinations.<\/p>\n\n\n\n
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Figure 3:\u00a0 An example of permutations if there are only 3 possibilities.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Factorial Identity and More:<\/h3>\n

The factorial 0! is defined as 1 for many of the same reasons that n0<\/sup> is equal to 1.\u00a0 The factorial 1! follows the same pattern, of 1 multiplied only one time.\u00a0 The other factorials grow rapidly, as can be seen by the diagram.<\/p>\n\n\n\n
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Figure 4:\u00a0 The value of factorials.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Choosing a Few Options:<\/h3>\n

Many times, all the possible permutations for all members in a system are not necessary.\u00a0 Suppose the task is just to place the first three runners in a race of 11 runners.\u00a0 All 11 participants have the possibility of getting first place, 10 participants have the possibility of getting second place, and 9 have the possibility of getting third place.\u00a0 There are 990 possible combinations of winners, or 11\u221910\u22199, compared to the entire possibility of 39,916,800 combinations down to 11th<\/sup> place.<\/p>\n

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Overview: Factorials involve all possible outcomes of an event.\u00a0 They are calculated by multiplying the number of possible events times the number of events minus 1 times the number of events minus 2 until there is only one possibility left. Figure 1:\u00a0 The factorial formula in mathematical symbols Example of a Factorial: Suppose four actresses […]<\/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":[644,1318],"class_list":["post-6982","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-factorials","tag-permutations"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6982","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6982"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6982\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6982"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6982"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6982"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}