ANSWER
[tex]^8P_4=1680[/tex]
EXPLANATION
The given permutation is
[tex]^8P_4.[/tex]
Recall the formula for permutation
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
We substitute n=8, and r=4 to obtain:
[tex]^8P_4=\frac{8!}{(8-4)!}[/tex]
[tex]^8P_4=\frac{8!}{4!}[/tex]
Recall the factorial expansion
[tex]n! = n \times (n - 1) \times (n - 2)...3 \times 2 \times 1[/tex]
We apply this expansion to get:
[tex]^8P_4=\frac{8 \times 7 \times 6 \times 5 \times 4!}{4!}[/tex]
[tex]^8P_4=8 \times 7 \times 6 \times 5[/tex]
[tex]^8P_4=1680[/tex]
