Answer
$252$
Work Step by Step
RECALL:
$C(n, r) = \dfrac{n!}{r!(n-r)!}$
Use the formula above to obtain:
$C(10, ,5) = \dfrac{10!}{5!(10-5)!}
\\C(10, 5) = \dfrac{10!}{5!(5!)}
\\C(10, 5) = \dfrac{10(9)(8)(7)(6)(5!)}{5\cdot 4\cdot3\cdot2\cdot1 \cdot 5!}$
Cancel the common factors to obtain:
$\require{cancel}
\\C(10, 5) = \dfrac{10(9)(8)(7)\cancel{(6)}\cancel{(5!)}}{5\cdot 4\cdot\cancel{3\cdot2\cdot1} \cdot \cancel{5!}}
\\C(10, 5)= \dfrac{\cancel{10}2 \cdot 9 \cdot \cancel{8}2 \cdot 7}{\cancel{5} \cdot \cancel{4}}
\\C(10, 5) = 252$
