Evaluate the expression  $_5P_2$5​P2​​ .$_5P_2=$5​P2​=​

The expression $_5P_2$ represents a permutation, which is a way to count the number of possible arrangements of a certain number of items from a larger set. In this case, we are looking at the number of ways to arrange 2 items from a set of 5.

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 choose,
• "!" denotes a factorial, which means multiplying all positive integers up to that number.

So, to evaluate $_5P_2$, we can plug in the numbers into the formula:

$_5P_2 = 5! / (5-2)!$

This simplifies to:

$_5P_2 = 5! / 3!$

To solve this, we first need to calculate the factorials.

5! = 5 * 4 * 3 * 2 * 1 = 120 3! = 3 * 2 * 1 = 6

Then we divide 120 by 6 to get the final answer:

$_5P_2 = 120 / 6 = 20$

So, $_5P_2 = 20$.