Question

use the formula for $_{n}p_{r}$ to evaluate the following expression.
$_{8}p_{8}$

$_{8}p_{8}=\square$

Explanation:

Step1: Recall permutation formula

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

Step2: Substitute values into formula

Substitute \(n = 8\) and \(r = 8\) into the formula: \(_{8}P_{8}=\frac{8!}{(8 - 8)!}\). Since \((8-8)!=0!\) and by definition \(0!=1\), the formula becomes \(_{8}P_{8}=\frac{8!}{1}\).

Step3: Calculate factorial

We know that \(n!=n\times(n - 1)\times\cdots\times1\). So \(8!=8\times7\times6\times5\times4\times3\times2\times1=40320\).

Answer:

\(40320\)