Question

evaluate the expression.
$_{12}p_3$
$_{12}p_3 = \square$
(simplify your answer.)

Explanation:

Step1: Recall Permutation Formula

The permutation formula is \( _nP_r=\frac{n!}{(n - r)!} \), where \( n = 12 \) and \( r = 3 \).

Step2: Substitute Values

Substitute \( n = 12 \) and \( r = 3 \) into the formula: \( _{12}P_3=\frac{12!}{(12 - 3)!}=\frac{12!}{9!} \).

Step3: Simplify Factorials

Since \( n!=n\times(n - 1)\times\cdots\times1 \), \( 12! = 12\times11\times10\times9! \). So \( \frac{12!}{9!}=\frac{12\times11\times10\times9!}{9!} \).

Step4: Cancel Common Terms

Cancel out \( 9! \) from numerator and denominator: \( 12\times11\times10 \).

Step5: Calculate the Product

Calculate \( 12\times11\times10 = 1320 \).

Answer:

1320