Question

evaluate each expression. sample problem ( _8p_3 ) ( \frac{8!}{(8-3)!} = \frac{8!}{5!} = 336 ) ( _6p_6 ) > enter the answer in the space provided. use numbers instead of words.

Explanation:

Step1: Recall permutation formula

The formula for permutations \( _nP_r \) is \( \frac{n!}{(n - r)!} \). For \( _6P_6 \), we have \( n = 6 \) and \( r = 6 \).

Step2: Substitute into formula

Substitute \( n = 6 \) and \( r = 6 \) into the formula: \( _6P_6=\frac{6!}{(6 - 6)!} \). Since \( 6-6 = 0 \) and \( 0!=1 \), this becomes \( \frac{6!}{1} \).

Step3: Calculate \( 6! \)

We know that \( n!=n\times(n - 1)\times\cdots\times1 \), so \( 6!=6\times5\times4\times3\times2\times1 = 720 \).

Answer:

720