Answer
$\frac{5_{{C}{_{1}}}.{7_{{C}{_{2}}}}}{12_{{C}{_{3}}}}$ = $\frac{21}{44}$
Work Step by Step
$\frac{5_{{C}{_{1}}}.{7_{{C}{_{2}}}}}{12_{{C}{_{3}}}}$ = $\frac{\frac{5!}{(5 - 1)!. 1!}\times{\frac{7!}{(7 - 2)!. 2!}}}{\frac{12!}{(12 - 3)!.3!}}$
= $\frac{\frac{5!}{4!. 1!}\times{\frac{7!}{5!. 2!}}}{\frac{12!}{9!.3!}}$
= $\frac{\frac{5\times4!}{4!. 1}\times{\frac{7\times6\times5!}{5!. 2}}}{\frac{12\times11\times10\times9!}{9!.3\times2\times1}}$
= $\frac{\frac{5}{1}\times{\frac{7\times6}{2}}}{\frac{12\times11\times10}{3\times2\times1}}$
= $\frac{5\times21}{2\times11\times10}$
= $\frac{105}{220}$
= $\frac{21}{44}$
