Question

evaluate the expression.
$_{8}p_{2}$

Explanation:

Step1: Recall permutation formula

The formula for permutations is \( _nP_r=\frac{n!}{(n - r)!} \), where \( n = 8 \) and \( r=2 \).

Step2: Substitute values into formula

Substitute \( n = 8 \) and \( r = 2 \) into the formula: \( _8P_2=\frac{8!}{(8 - 2)!}=\frac{8!}{6!} \)

Step3: Simplify factorials

We know that \( n!=n\times(n - 1)\times\cdots\times1 \), so \( 8! = 8\times7\times6! \). Then \( \frac{8!}{6!}=\frac{8\times7\times6!}{6!} \)

Step4: Cancel out common terms

Cancel out \( 6! \) from numerator and denominator: \( 8\times7 = 56 \)

Answer:

56