Answer
$\displaystyle \frac{21}{44}$
Work Step by Step
${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$
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${}_{5}C_{1}=\displaystyle \frac{5!}{(5-1)!1!}=5$
${}_{7}C_{2}=\displaystyle \frac{7!}{(7-2)!2!}=\frac{7\times 6}{1\times 2}=21$
${}_{12}C_{3}=\displaystyle \frac{12!}{(12-3)!3!}=\frac{12\times 11\times 10}{1\times 2\times 3}$
$=2\times 11\times 10=220$
$\displaystyle \frac{{}_{5}C_{1}\cdot {}_{7}C_{2}}{{}_{12}C_{3}}=\frac{5\times 21}{220}=\frac{21}{44}$
