In Problems 11–18, find the value of each permutation.
9P4

Verified step by step guidance

1. Understand that the notation \(nP r\) represents the number of permutations of \(n\) items taken \(r\) at a time, where order matters.
2. Recall the formula for permutations: \(nP r = \frac{n!}{(n - r)!}\), where \(n!\) denotes the factorial of \(n\).
3. Identify the values from the problem: here, \(n = 9\) and \(r = 4\).
4. Substitute these values into the formula: \$9P4 = \frac{9!}{(9 - 4)!} = \frac{9!}{5!}$.
5. Calculate the factorial expressions or simplify by expanding the numerator and denominator to find the number of permutations.

Key Concepts

Permutation

A permutation refers to the arrangement of objects in a specific order. It counts the number of ways to order a subset of items from a larger set, where order matters. For example, arranging 4 books out of 9 in a row is a permutation problem.

Permutation Formula

The permutation formula is given by nPr = n! / (n - r)!, where n is the total number of items and r is the number of items to arrange. This formula calculates the number of ordered arrangements of r items selected from n.

Factorial

Factorial, denoted by n!, is the product of all positive integers up to n. It is used in permutations to calculate the total number of ways to arrange items. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.