In Exercises 1–8, use the formula for nPr to evaluate each expression. 8P0

Verified step by step guidance

1. Understand that the notation \( nP0 \) represents the number of permutations of \( n \) items taken 0 at a time.
2. Recall the formula for permutations: \( nPr = \frac{n!}{(n-r)!} \).
3. Substitute \( n = 8 \) and \( r = 0 \) into the formula: \( 8P0 = \frac{8!}{(8-0)!} \).
4. Simplify the expression: \( 8P0 = \frac{8!}{8!} \).
5. Recognize that any number divided by itself is 1, so \( 8P0 = 1 \).

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 involving arrangements and selections in various contexts.

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 permutations and combinations, as they help calculate the total arrangements of items. For example, 5! equals 5 × 4 × 3 × 2 × 1 = 120.

Zero Factorial

Zero factorial, denoted as 0!, is defined to be equal to 1. This definition is essential in combinatorial mathematics, particularly in permutations and combinations, as it allows for consistent calculations when selecting zero items from a set. Understanding this concept is key to evaluating expressions like nP0.