Use the formula for _nP_r to evaluate each expression. ₉P₄

검증된 단계별 안내

Recall the formula for permutations: $nP_r = \frac{n!}{(n-r)!}$, where $n$ is the total number of items and $r$ is the number of items to arrange.

Identify the values of $n$ and $r$ from the problem: here, $n = 9$ and $r = 4$.

Substitute these values into the formula: $9P4 = \frac{9!}{(9-4)!} = \frac{9!}{5!}$.

Write out the factorial expressions to simplify: $9! = 9 \times 8 \times 7 \times 6 \times 5!$, so $\frac{9!}{5!} = \frac{9 \times 8 \times 7 \times 6 \times 5!}{5!}$.

Cancel the common \$5!$ terms to get $9P4 = 9 \times 8 \times 7 \times 6$, which you can then multiply to find the final value.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Permutation (nPr)

A permutation refers to the arrangement of objects in a specific order. The notation nPr represents the number of ways to arrange r objects out of n distinct objects, where order matters.

Permutation Formula

The formula for permutations is nPr = n! / (n - r)!, where n! denotes the factorial of n. This formula calculates the total number of ordered arrangements of r items selected from n.

Factorial Function

The factorial of a positive integer n, written as n!, is the product of all positive integers from 1 to n. It is essential in permutation calculations to determine the number of possible arrangements.

Use the formula for nPr to evaluate each expression. 9P4