Question

evaluate the given expression.
p(8, 6)

Explanation:

Step1: Recall permutation formula

The permutation formula is $P(n, k) = \frac{n!}{(n-k)!}$, where $n=8$, $k=6$.

Step2: Substitute values into formula

$P(8, 6) = \frac{8!}{(8-6)!} = \frac{8!}{2!}$

Step3: Expand factorials and simplify

$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2!$, so $\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2!}{2!} = 8 \times 7 \times 6 \times 5 \times 4 \times 3$

Step4: Calculate the product

$8 \times 7 = 56$; $56 \times 6 = 336$; $336 \times 5 = 1680$; $1680 \times 4 = 6720$; $6720 \times 3 = 20160$

Answer:

20160