ANSWER
[tex]8P_4 = 1680[/tex]
EXPLANATION
We use the formula
[tex]nP_r = \frac{n!}{(n - r)!} [/tex]
For
[tex]8P_4[/tex]
and n=8, r=4.
[tex]8P_4= \frac{8!}{(8- 4)!} [/tex]
This simplifies to
[tex]8P_4= \frac{8!}{4!} [/tex]
We expand the numerator using factorial notation,
[tex]8P_4= \frac{8 \times 7 \times 6 \times 5 \times 4!}{4!} [/tex]
The common factors cancel out.
[tex]8P_4= 8 \times 7 \times 6 \times 5[/tex]
[tex]8P_4= 1680[/tex]
