Question

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

Answer 1

`^8P_4=1680`

Step-by-step explanation

The given permutation is

`^8P_4.`

Recall the formula for permutation

`^nP_r=(n!)/((n-r)!)`

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

`^8P_4=(8!)/((8-4)!)`

`^8P_4=(8!)/(4!)`

Recall the factorial expansion

`n! = n * (n - 1) * (n - 2)...3 * 2 * 1`

We apply this expansion to get:

`^8P_4=(8 * 7 * 6 * 5 * 4!)/(4!)`

`^8P_4=8 * 7 * 6 * 5`

`^8P_4=1680`