Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 8

$36$

According to the binomial theorem, we have: $\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$. Substitute $9$ for $n$ and $7$ for $k$ in the above formula. Therefore, $\dbinom{9}{7}=\dfrac{9!}{7! \ (9-7)!} \\ =\dfrac{9!}{7! \ 2!}\\=\dfrac{ 9 \cdot 8 \cdot 7!}{7 ! (2 \cdot 1)}\\= 36 $