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Chapter 11: Problem 57

What is a permutation?

Short Answer

Expert verified
A permutation is an arrangement of all the members of a set into some sequence or order. The order or arrangement is significant in permutations.

Step by step solution

01

Definition

A permutation is an arrangement of all the members of a set into some sequence or order. In other words, one of the possible arrangements of a collection where order matters.
02

Elaboration

For instance, if we have three different numbers: 1, 2, and 3. We can arrange those in different ways like (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1). These are all different permutations of the set {1, 2, 3}. Similarly, letters in a word can also create permutations, for example, all the permutations of the word 'DOG' are 'DOG', 'DGO', 'ODG', 'OGD', 'GDO', and 'GOD'.
03

Summary

Permutations apply when we care about the order of things. It could be numbers, letters, people, and anything where the order or arrangement is a crucial factor. It is an important concept in combinatorics, statistics, and many areas in mathematics and computer science as well.

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