In a statistics book I'm studying, I'm given the following:
$\frac{\binom{8}{3}}{\binom{10}{3}}=\frac{\frac{8!}{3!5!}}{\frac{10!}{3!7!}}=\frac{8\times7\times6}{10\times9\times8}=\frac{42}{90}=0.47$
I don't understand how $\frac{\frac{8!}{3!5!}}{\frac{10!}{3!7!}}$ became $\frac{8\times7\times6}{10\times9\times8}$.
What's the trick used here?
$$\frac{8!}{5!}=\frac{8 \times 7 \times 6 \times 5!}{5!}=8 \times 7 \times 6$$
$$\frac{10!}{7!}=\frac{10 \times 9 \times 8 \times 7!}{7!}= 10 \times 9 \times 8$$
$3!$ terms get canceled out.