Question

Compute the permutation. 8 P 4 32 1,680 6,720

Answer 1

ANSWER

$^8P_4=1680$

EXPLANATION

The given permutation is

$^8P_4.$

Recall the formula for permutation

$^nP_r=\frac{n!}{(n-r)!}$

We substitute n=8, and r=4 to obtain:

$^8P_4=\frac{8!}{(8-4)!}$

$^8P_4=\frac{8!}{4!}$

Recall the factorial expansion

$n! = n \times (n - 1) \times (n - 2)...3 \times 2 \times 1$

We apply this expansion to get:

$^8P_4=\frac{8 \times 7 \times 6 \times 5 \times 4!}{4!}$

$^8P_4=8 \times 7 \times 6 \times 5$

$^8P_4=1680$