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 MISSISSIPPI. There are 11 letters. So n = 11 The letter M appears 1 times in the word. The letter I appear 4 times in the word. The letter S appears 4 times in the word. The letter P appears 2 times in the word. There is 4 the number of distinguishable letters. So k = 4 . The terms n 1 , n 2 , n 3 , n 4 represent the number of times a letters M, I, S, P appear in the word

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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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 37PS

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Number of possible permutations of the word MISSISSIPPI.

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Chapter 12.1, Problem 36PS

Chapter 12.1, Problem 38PS

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Nature of Mathematics (MindTap Course List)

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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