Answer
$\frac{_{10}C_{7}}{_{14}C_{7}}=\frac{5}{143}\approx0.035$
Work Step by Step
$_{n}C_{r}=\frac{n!}{(n-r)!r!}$
$_{10}C_{7}=\frac{10!}{(10-7)!7!}=\frac{10\times9\times8\times7!}{3!\times7!}=\frac{10\times9\times8}{3\times2\times1}=120$
$_{14}C_{7}=\frac{14!}{(14-7)!7!}=\frac{14\times13\times12\times11\times10\times9\times8\times7!}{7!\times7!}=\frac{14\times13\times12\times11\times10\times9\times8}{7\times6\times5\times4\times3\times2\times1}=3432$
$\frac{_{10}C_{7}}{_{14}C_{7}}=\frac{120}{3432}=\frac{5}{143}\approx0.035$
