Problem 62 - College Algebra

Question

Describe what \(_{n} P_{r}\) represents.

Step-by-Step Solution

Answer

\(_{n} P_{r}\) represents the number of permutations or ways to arrange \(r\) distinct elements from a set of \(n\) distinct elements. The formula for \(_{n} P_{r}\) is \( \frac{n!}{(n-r)!} \).

Step 1: Understand what Permutation is

First, it's important to understand what permutation means in combinatorics. Permutation refers to the arrangement of objects in a specific order. It matters where each object is placed. For example, 'ABC' and 'CBA' are two different permutations of the same set of elements.

Step 2: Apply Permutation to the term \(_{n} P_{r}\)

\(_{n} P_{r}\), often read as 'n permute r', is a formula used to calculate the number of permutations or ways to arrange \(r\) distinct elements from a set of \(n\) distinct elements. The order of arrangement is important in permutation.

Step 3: Compute \(_{n} P_{r}\) formula

The formula for \(_{n} P_{r}\) is \( \frac{n!}{(n-r)!} \), where \(n!\) signifies the factorial of \(n\) - the product of all positive integers from 1 to \(n\), and \((n-r)!\) is the factorial of \((n-r)\).