Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and Binomial Theorem - 10.2 Exercises - Skill Practice - Page 695: 45

See below.

We know that $_nC_r=\frac{n!}{r!(n-r)!}$ and $_nP_r=\frac{n!}{(n-r)!}$. Hence $_nC_1=\frac{n!}{1!(n-1)!}=\frac{n\cdot(n-1)!}{(n-1)!}=n=\frac{n\cdot(n-1)!}{(n-1)!}=\frac{n!}{(n-1)!}=_nP_1$ Thus we proved what we had to.