Answer
$_{12}C_3=220$
Work Step by Step
RECALL:
$_nC_r = \dfrac{n!}{r!(n-r)!}$
Use this definition to have:
$\require{cancel}
_{12}C_3=\dfrac{12!}{3!(12-3)!}
\\_{12}C_3=\dfrac{12!}{3!(9!)}
\\_{12}C_3 = \dfrac{12(11)(10)(9!)}{3!(9!)}
\\_{12}C_3 = \dfrac{12(11)(10)\cancel{(9!)}}{3!\cancel{(9!)}}
\\_{12}C_3=\dfrac{12(11)(10)}{3!}
\\_{12}C_3=\dfrac{12(11)(10)}{6}
\\_{12}C_3=\dfrac{2\cancel{12}(11)(10)}{\cancel{6}}
\\_{12}C_3=220$
