Problem 76 - College Algebra

Question

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

Step-by-Step Solution

Answer

\(_{n}P_{r}\) represents the number of permutations, or distinct ways to arrange \(r\) items out of \(n\) total unique items.

Step 1: Define Permutations

Permutations refer to the arrangement of a set of objects, where the order of the objects is important.

Step 2: Break down the notation

In the notation \(_{n}P_{r}\), \(n\) and \(r\) refer to the total number of items to choose from and the number of items being chosen, respectively.

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

\(_{n}P_{r}\) specifically represents the number of ways to arrange \(r\) items out of a total of \(n\) unique items. It is calculated as \(n! / (n - r)!\), where '!' denotes a factorial, which is the product of all positive integers up to that number.