Explanation Factorial: Factorial gives the product of an integer and all the integers below it. Factorial is denoted by a positive integer and an exclamation point. For any counting number n, the factorial of n is defined by n ! = n ( n − 1 ) ( n − 2 ) ⋅ ⋯ ⋅ 3 ⋅ 2 ⋅ 1 0 ! = 1 Example: The factorial of 4 is 4 ! = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24 This is called as multiplication property of factorial or countdown property. Permutation: Permutation is the process of arranging the objects of a set in a definite order. If the set is already arranged, we can rearrange the objects using permutation. In permutation, repetition of object is allowed. It selects the objects regardless of the order. The permutation formula for the number of permutations possible for the choices r object from the set of n distinct object is n P r = n ! ( n − r ) ! Where, n- Number of distinct object in the set r- Number of choices Calculation: There are 80 people. The TV program selects three contestants from 80 audiences. So n = 80 ; r = 3 Number of possibilities is obtained by calculating 80 P 3 . The number of permutation is given by, n P r = n ! ( n − r ) !

Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

13th Edition

ISBN: 9781337605076

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 12.1, Problem 59PS

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Time taken by the program to select all the possibilities.

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Chapter 12.1, Problem 58PS

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Chapter 12 Solutions

Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

Ch. 12.1 - IN YOUR OWN WORDS What is a permutation? What is...Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P2 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P4 Ch. 12.1 - Prob. 8PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 52P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 4P4

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Time taken by the program to select all the possibilities.

Solution Summary: The author explains that factorial gives the product of an integer and all the integers below it. Permutation is the process of arranging the objects in a definite order.

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Time taken by the program to select all the possibilities.