Answer
$36$
Work Step by Step
RECALL:
$C(n, r) = \dfrac{n!}{r!(n-r)!}$
Use the formula above to obtain:
$C(9, 2) = \dfrac{9!}{2!(9-2)!}
\\C(9, 2) = \dfrac{9!}{2!(7!)}
\\C(9, 2) = \dfrac{9(8)(7!)}{2 \cdot 1(7!)}$
Cancel the common factors to obtain:
$\require{cancel}
\\C(9, 2) = \dfrac{9\cancel{(8)}4\cancel{(7!)}}{\cancel{2 \cdot 1}\cancel{(7!)}}
\\C(9, 2) = 36$
