Answer
(a) 120
(b) 720
(c) 8
(d) 6720
(e) 40320
(f) 3628800
Work Step by Step
We apply the formula $P(n, r)=\frac{n!}{(n-r)!}$ to find
(a) $P(6, 3)=\frac{6!}{(6-3)!}=\frac{6!}{3!}=120$
(b) $P(6, 5)=\frac{6!}{(6-5)!}=\frac{6!}{1!}=720$
(c) $P(8, 1)=\frac{8!}{(8-1)!}=\frac{8!}{7!}=8$
(d) $P(8, 5)=\frac{8!}{(8-5)!}=\frac{8!}{3!}=6720$
(e) $P(8, 8)=\frac{8!}{(8-8)!}=\frac{8!}{0!}=40320$
(f) $P(10, 9)=\frac{10!}{(10-9)!}=\frac{10!}{1!}=3628800$
