Problem 75 - College Algebra

Question

What is a permutation?

Step-by-Step Solution

Answer

A permutation is the number of ways a set of objects, items, or numbers can be arranged in a specific order. It's used when arrangements are considered important.

Step 1: Understanding the Concept

Permutation is a mathematical term that represents the number of ways a set of objects, items, or numbers can be arranged in a specific order. In more concrete terms, if you're given a set of 'n' objects, a permutation of these objects is any possible arrangement of the objects in a line.

Step 2: Examples to Illustrate the Concept

A good everyday example of permutation is the arrangement of books on a shelf. If you have 5 different books, and you want to know how many ways they can be arranged in a row on a shelf, this is precisely what a permutation tells you. Similarly, take the arrangement of letters in a word - for a 3-letter word like 'CAT', there are 6 possible permutations: CAT, CTA, ACT, ATC, TCA, and TAC.

Step 3: Applying the concept

In math, the formula for permutation is usually applied when specific arrangements are important. This formula is given by the expression \(P(n, r) = n! / (n-r)!\), where \(n\) is the total number of items, \(r\) is the number of items to choose for each arrangement, and \(n!\) denotes the factorial of \(n\).