Answer
$330$
Work Step by Step
RECALL:
$C(n, r) = \dfrac{n!}{r!(n-r)!}$
Use the formula above to obtain:
$C(11, 4) = \dfrac{11!}{4!(11-4)!}
\\C(11, 4) = \dfrac{11!}{4!(7!)}
\\C(11, 4) = \dfrac{11(10)(9)(8)(7!)}{4\cdot3\cdot2\cdot1 \cdot 7!}$
Cancel the common factors to obtain:
$\require{cancel}
\\C(11, 4) = \dfrac{11(10)(9)\cancel{(8)}\cancel{(7!)}}{\cancel{4}\cdot3\cdot\cancel{2}\cdot1 \cdot \cancel{7!}}
\\C(11, 4) = \dfrac{11(10)\cancel{(9)}3}{\cancel{3}}
\\C(11, 4) = 330$
