Problem 61 - College Algebra

Question

What is a permutation?

Step-by-Step Solution

Answer

A permutation is an arrangement of objects in a specific order. It is mathematically represented as \(nPr\), the formula for calculating permutations being \(nPr = n! / (n-r)!\)

Step 1: Defining a Permutation

A permutation is an arrangement of objects in a particular order. For example, if there are three objects, say A, B and C, they can be arranged in a specific order, such as CAB, BCA, ABC, etc. Each of these arrangements is called a permutation.

Step 2: Mathematical Representation of a Permutation

Mathematically, a permutation is represented as \(nPr\), where \(n\) is the total number of objects and \(r\) is the number of objects taken at a time. The formula to calculate permutations is \(nPr = n! / (n-r)!\), where \( ! \) represents factorial - the product of an integer and all the numbers less than it, down to 1.

Step 3: Example of a Permutation

For instance, if there are three objects as A, B and C, the permutations (or the different arrangements) for three objects taken two at a time (\(3P2\)) are AB, BA, AC, CA, BC, and CB.