Use the formula for _nP_r to evaluate each expression. ₈P₅

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, $n = 8$ and $r = 5$.

Substitute these values into the formula: $8P_5 = \frac{8!}{(8-5)!} = \frac{8!}{3!}$.

Write out the factorial expressions explicitly: $8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3!$, so $\frac{8!}{3!} = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3!}$.

Cancel the common \$3!$ terms in numerator and denominator, leaving $8P_5 = 8 \times 7 \times 6 \times 5 \times 4$, which you can multiply to find the final answer.

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주요 개념

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

Permutation (nPr)

A permutation represents the number of ways to arrange a subset of items from a larger set where order matters. The notation nPr denotes the number of permutations of n items taken r at a time.

Permutation Formula

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

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 for computing permutations and combinations in algebra.

Use the formula for nPr to evaluate each expression. 8P5