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 COMBINATORICS. There are 13 letters. So n = 13 The letter C, O, and I appears 2 times in the word. The letter M, B, N, A, T, R, S appears 1 times in the word. There is 10 the number of distinguishable letters. So k = 10 . The terms n 1 , n 2 , n 3 , n 4 , n 5 , n 6 , n 7 , n 8 , n 9 , n 10 represent the number of times a letters C, O, M, B, I, N, A, T, R, S appear in the word

13th Edition

ISBN: 9780357127193

Author: SMITH

Publisher: CENGAGE L

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of …

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Chapter 12.1, Problem 42PS

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Number of possible permutations of the word COMBINATORICS.

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Chapter 12 Solutions

NATURE OF MATHEMATICS WEBASSIGN ACCESS

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 COMBINATORICS.

Solution Summary: The author explains that the number of possible permutations of the word COMBINATORICS is 778,377,600.

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Number of possible permutations of the word COMBINATORICS.