Evaluate the expression  $_{12}P_0$12​P0​​ .$_{12}P_0=$12​P0​=​

The expression $_{12}P_0$ represents the number of ways to arrange 0 items from a set of 12.

The formula for permutations is given by:

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

where:

• n is the total number of items,
• r is the number of items to choose,
• "!" denotes factorial, which is the product of all positive integers up to that number.

Substituting n=12 and r=0 into the formula gives:

$_{12}P_0 = 12! / (12-0)! = 12! / 12!$

Any number divided by itself is 1, so:

$_{12}P_0 = 1$

Therefore, there is only 1 way to arrange 0 items from a set of 12.