Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.5 The Binomial Theorem - 12.5 Assess Your Understanding - Page 837: 45

Refer to the step by step section below.

Recall: ${n\choose j}=\dfrac{n!}{(n-j)!j!}$. Hence, \begin{align*} \require{cancel} {n\choose n-1}&=\dfrac{n!}{(n-(n-1)!(n-1)!}\\ &=\dfrac{n\cdot(n-1)!}{1!(n-1)!}\\ &=\dfrac{n\cancel{\cdot(n-1)!}}{\cancel{(n-1)!}}\\ &=n\end{align*} \begin{align*} \require{cancel} {n\choose n}&=\dfrac{n!}{(n-(n))!(n)!}\\ &=\dfrac{n!}{0!(n)!}\\ &=1\end{align*}