Problem 75 - Algebra and Trigonometry

Question

What is a permutation?

Step-by-Step Solution

Answer

A permutation refers to the arrangement or rearrangement of items in a specific order. It varies in types based on whether the arrangement allows repetition of elements or not. The term permutation also implies the action of changing the order of the elements in an ordered set.

Step 1: Definition

In mathematics, a permutation of a set is, loosely, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word 'permutation' also refers to the act or process of changing the linear order of an ordered set.

Step 2: Distinguish from combinations

Permutations differ from combinations, which are selections of some members of a set with no regard to the order they are in when selected.

Step 3: Permutations with repetition

When the members of a set can be repeated in a permutation, it is called a permutation with repetition. For example, in the set of numbers {1, 2}, the possible permutations with repetition for a sequence of two numbers are: {1, 1}, {1, 2}, {2, 1}, {2, 2}.

Step 4: Permutations without repetition

When the members of a set cannot be repeated in a permutation, it is called a permutation without repetition. For example, in the set of numbers {1, 2}, the possible permutations without repetition for a sequence of two numbers are: {1, 2}, {2, 1}