Answer
$156,849$
Work Step by Step
RECALL:
$C(n, r) = \dfrac{n!}{r!(n-r)!}$
Use the formula above to obtain:
$C(99, 3) = \dfrac{99!}{3!(99-3)!}
\\C(99, 3)) = \dfrac{99!}{3!(96!!)}
\\C(99, 3) = \dfrac{99(98)(97)(96!)}{3\cdot2\cdot1 \cdot 96!}$
Cancel the common factors to obtain:
$\require{cancel}
\\C(99, 3) = \dfrac{\cancel{99}33\cancel{(98}49)(97)\cancel{(96!)}}{\cancel{3}\cdot\cancel{2}\cdot1 \cdot \cancel{96!}}
\\C(99, 3) = 156,849$
