Chapter 7 - Section 7.4 - The Binomial Theorem - 7.4 Exercises - Page 664: 11

$n$

Using $\left( \array{n\\r} \right)=\dfrac{n!}{r!(n-r)!},$ the given expression, $\left( \array{ n\\n-1 } \right)$ evaluates to \begin{array}{l}\require{cancel} =\dfrac{n!}{(n-1)!(n-(n-1))!} \\\\= \dfrac{n(n-1)!}{(n-1)!(n-n+1)!} \\\\= \dfrac{n\cancel{(n-1)!}}{\cancel{(n-1)!}(1)} \\\\= n \end{array}