Evaluate the expression  $_7P_3$7​P3​​ .$_7P_3=$7​P3​=​

The expression $_7P_3$ represents a permutation, which is a way to arrange a certain number of items out of a larger set, where the order of arrangement matters.

Here's how you can evaluate $_7P_3$:

Step 1: Understand the notation. In general, $_nP_r$ = n! / (n - r)!. Here, n is the total number of items, and r is the number of items to choose.

Step 2: Substitute the given values into the formula. So, $_7P_3$ = 7! / (7 - 3)!.

Step 3: Simplify the expression. This gives you 7! / 4!.

Step 4: Calculate the factorials. 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040, and 4! = 4 * 3 * 2 * 1 = 24.

Step 5: Divide 5040 by 24 to get the final answer. $_7P_3$ = 5040 / 24 = 210.

So, $_7P_3$ = 210.