Answer
$_{10}C_2=45$
Work Step by Step
RECALL:
$_nC_r = \dfrac{n!}{r!(n-r)!}$
Use this definition to have:
$\require{cancel}
_{10}C_2=\dfrac{10!}{2!(10-2)!}
\\_{10}C_2=\dfrac{10!}{2!(8!)}
\\_{10}C_2 = \dfrac{10(9)(8!)}{2!(8!)}
\\_{10}C_2 = \dfrac{10(9)\cancel{(8!)}}{2!\cancel{(8!)}}
\\_{10}C_2=\dfrac{10(9)}{2}
\\_{10}C_2=\dfrac{5\cancel{10}(9)}{\cancel{2}}
\\_{10}C_2=45$
