## Thinking Mathematically (6th Edition)

$\displaystyle \frac{3}{68}$
${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$ -------- ${}_{4}C_{2}=\displaystyle \frac{4!}{(4-2)!2!}=\frac{4\times 3}{1\times 2}=6$ ${}_{6}C_{1}=\displaystyle \frac{6!}{(6-1)!1!}=6$ ${}_{18}C_{3}=\displaystyle \frac{18!}{(18-3)!3!}=\frac{18\times 17\times 16}{1\times 2\times 3}$ $=3\times 17\times 16=816$ $\displaystyle \frac{{}_{4}C_{2}\cdot {}_{6}C_{1}}{{}_{18}C_{3}}=\frac{6\times 6}{816}=\frac{3}{68}$