Answer
$462$
Work Step by Step
RECALL:
$C(n, r)= \dfrac{n!}{r!(n-r)!}$
Using the definition above gives:
$\require{cancel}
C(11, 5)!
\\= \dfrac{11!}{5!(11-5)!}
\\=\dfrac{11!}{5!6!}
\\=\dfrac{11(10)(9)(8)(7)(6!)}{5(4)(3)(2)(1)6!}
\\=\dfrac{11(10)(9)\cancel{(8)}(7)\cancel{(6!)}}{5\cancel{(4)}(3)\cancel{(2)}(1)\cancel{6!}}
\\=\dfrac{11\cancel{(10)}^2\cancel{(9)}^3(7)}{\cancel{5}\cancel{(3)}(1)}
\\=462$
