Answer
$\frac{4_{{C}{_{2}}}.{6_{{C}{_{1}}}}}{18_{{C}{_{3}}}}$ = $\frac{3}{68}$
Work Step by Step
$\frac{4_{{C}{_{2}}}.{6_{{C}{_{1}}}}}{18_{{C}{_{3}}}}$ = $\frac{\frac{4!}{(4 - 2)!. 2!}\times{\frac{6!}{(6 - 1)!. 1!}}}{\frac{18!}{(18 - 3)!.3!}}$
= $\frac{\frac{4!}{2!. 2!}\times{\frac{6!}{5!. 1!}}}{\frac{18!}{15!.3!}}$
= $\frac{\frac{4\times3\times2!}{2!. 2\times1}\times{\frac{6\times5!}{5!. 1}}}{\frac{18\times17\times16\times15!}{15!.3\times2\times1}}$
= $\frac{\frac{4\times3}{2\times1}\times{\frac{6}{1}}}{\frac{18\times17\times16}{3\times2\times1}}$
= $\frac{6\times6}{3\times17\times16}$
= $\frac{36}{816}$
= $\frac{3}{68}$
