Question

use the formula for $_np_r$ to evaluate the following expression.
$_8p_3$

$_8p_3 = \square$

Explanation:

Step1: Recall permutation formula

The formula for permutation is \(_{n}P_{r}=\frac{n!}{(n - r)!}\). Here \(n = 8\) and \(r=3\).

Step2: Substitute values into formula

\(_{8}P_{3}=\frac{8!}{(8 - 3)!}=\frac{8!}{5!}\).

Step3: Expand factorials

Since \(n!=n\times(n - 1)\times\cdots\times1\), then \(8! = 8\times7\times6\times5!\). So \(\frac{8!}{5!}=\frac{8\times7\times6\times5!}{5!}\).

Step4: Simplify the expression

Cancel out the \(5!\) terms. We get \(8\times7\times6\).

Step5: Calculate the product

\(8\times7\times6=336\).

Answer:

\(336\)