In Exercises 1–8, use the formula for nPr to evaluate each expression. 8P5

Key Concepts

Permutations

Permutations refer to the different ways of arranging a set of items where the order matters. The notation nPr represents the number of ways to choose and arrange r items from a total of n items. Understanding permutations is crucial for solving problems that involve ordered selections.

Factorial

The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers up to n. Factorials are fundamental in calculating permutations and combinations, as they provide the total number of arrangements or selections possible. For example, 5! equals 5 × 4 × 3 × 2 × 1 = 120.

nPr Formula

The formula for permutations, nPr, is given by nPr = n! / (n - r)!. This formula calculates the number of ways to arrange r items from a set of n items. It is essential for solving problems that require determining the number of ordered arrangements, such as in the given expression 8P5.