Answer
$_{48}C_3=17,296$
Work Step by Step
RECALL:
$_nC_r = \dfrac{n!}{r!(n-r)!}$
Use this definition to have:
$\require{cancel}
_{48}C_3=\dfrac{48!}{3!(48-3)!}
\\_{48}C_3=\dfrac{48!}{3!(45!)}
\\_{48}C_3 = \dfrac{48(47)(46)(45!)}{3!(45!)}
\\_{48}C_3 = \dfrac{48(47)(46)\cancel{(45!)}}{6\cancel{(45!)}}
\\_{48}C_3 = \dfrac{8\cancel{48}(47)(46)}{\cancel{6}}
\\_{48}C_3=17,296$
