Answer
$56$
Work Step by Step
RECALL:
$C(n, r) = \dfrac{n!}{r!(n-r)!}$
Use the formula above to obtain:
$C(8, 3) = \dfrac{8!}{3!(8-3)!}
\\C(8, 3) = \dfrac{8!}{3!(5!)}
\\C(8, 3) = \dfrac{8(7)(6)(5!)}{3\cdot 2 \cdot 1(5!)}$
Cancel the common factors to obtain:
$\require{cancel}
\\C(8, 3) = \dfrac{8(7)\cancel{(6)}(\cancel{5!})}{\cancel{3\cdot 2 \cdot 1}\cancel{(5!)}}
\\C(8, 3) = 56$
