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 Distinguishable 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. Distinguishable permutation is the special case of permutation where the permutations (arrangements) can be distinguished from one another. In distinguishable permutation, repetition of object is allowed but they must be distinguishable. It selects the objects regardless of the order. Formula for distinguishable permutation: Consider a set of n objects in which n 1 are of one kind, n 2 are of another kind, ⋯ and n k are of further kind. The number of distinguishable permutation= n ! n 1 ! n 2 ! ⋅ ⋯ ⋅ n k ! Where n = n 1 + n 2 + ⋯ + n k Calculation: We need to find the number of possible permutations of the word GRAMMATICAL. There are 11 letters. So n = 11 The letter A appears 3 times in the word. The letter M appears 2 times in the word. The letter G, R, T, I, C, L appears 1 times in the word. There is 8 the number of distinguishable letters. So k = 8 . The terms n 1 , n 2 , n 3 , n 4 , n 5 , n 6 , n 7 , n 8 represent the number of times a letters G, R, A, M, T, I, C, L appear in the word

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 40PS

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Number of possible permutations of the word GRAMMATICAL.

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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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Number of possible permutations of the word GRAMMATICAL.

Solution Summary: The author explains that the number of possible permutations of the word GRAMMATICAL is 3,326,400.

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To find: Number of possible permutations of the word GRAMMATICAL.

Chapter 12 Solutions

To find:

Number of possible permutations of the word GRAMMATICAL.