Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.5 The Binomial Theorem - 12.5 Assess Your Understanding - Page 836: 9

$50$

Recall: ${n\choose j}=\dfrac{n!}{(n-j)!j!}$. Hence, \begin{align*} \require{cancel} {50\choose 49}&=\dfrac{50!}{(50-49)!49!}\\ &=\dfrac{50!}{1!49!}\\ &=\dfrac{50\cdot49!}{49!}\\ &=\dfrac{50\cdot\cancel{49!}}{\cancel{49!}}\\ &=\dfrac{50}{1}\\ &=50\end{align*}