Evaluate the expression  $_8P_6$8​P6​​ .$_8P_6=$8​P6​=​

The expression $_8P_6$ represents a permutation, which is a way to arrange a certain number of items out of a larger set. In this case, we are arranging 6 items out of a set of 8.

The formula for a permutation is:

$_nP_r = n! / (n - r)!$

where:

• n is the total number of items,
• r is the number of items to arrange,
• "!" denotes a factorial, which means to multiply a number by every number less than it down to 1.

So, to evaluate $_8P_6$, we can plug the numbers into the formula:

$_8P_6 = 8! / (8 - 6)!$

First, calculate the factorials:

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320 2! = 2 * 1 = 2

Then, divide 8! by 2!:

$_8P_6 = 40320 / 2 = 20160$

So, $_8P_6 = 20160$.