Evaluate the expression  $_6P_5$6​P5​​ .$_6P_5=$6​P5​=​

The expression $_6P_5$ 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 5 items out of a set of 6.

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 $_6P_5$, we can plug the numbers into the formula:

$_6P_5 = 6! / (6 - 5)!$

This simplifies to:

$_6P_5 = 6! / 1!$

The factorial of 6 is 720 (6 * 5 * 4 * 3 * 2 * 1), and the factorial of 1 is 1, so:

$_6P_5 = 720 / 1 = 720$

So, $_6P_5 = 720$.