Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 9

$50$

According to the binomial theorem, we have: $\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$. Substitute $50$ for $n$ and $49$ for $k$ in the above formula. Therefore, $\dbinom{50}{49}=\dfrac{50!}{49! \ (50-49)!} \\ =\dfrac{50!}{1! \ 49!}\\=\dfrac{ 50 \cdot 49!}{49 ! }\\= 50 $