Answer
(a) 5
(b) 10
(c) 70
(d) 1
(e) 1
(f) 924
Work Step by Step
We apply the formula $C(n,r)=\frac{n!}{r!(n−r)!}$ to find
a) $C(5,1) = \frac{5!}{1!(5−1)!}$ = 5
b) $C(5,3) = \frac{5!}{3!(5−3)!}$ = 10
c) $C(8,4) = \frac{8!}{4!(8−4)!}$ = 70
d) $C(8,8) = \frac{8!}{8!(8−8)!}$ = 1
e) $C(8,0) = \frac{8!}{0!(8−0)!}$ = 1
f) $C(12,6) = \frac{12!}{6!(12−6)!}$ = 924