Chapter 7 - Section 7.4 - The Binomial Theorem - 7.4 Exercises - Page 664: 18

$5$

Using $_nC_r=\dfrac{n!}{r!(n-r)!},$ the given expression, $ _{5}C_{1} $ evaluates to \begin{array}{l}\require{cancel} =\dfrac{5!}{1!(5-1)!} \\\\= \dfrac{5!}{1!4!} \\\\= \dfrac{5(4!)}{(1)(4!)} \\\\= \dfrac{5(\cancel{4!})}{(1)(\cancel{4!})} \\\\= \dfrac{5}{1} \\\\= 5 \end{array}