Chapter 7 - Section 7.4 - The Binomial Theorem - 7.4 Exercises - Page 664: 12

$\dfrac{n(n-1)}{2}$

Using $\left( \array{n\\r} \right)=\dfrac{n!}{r!(n-r)!},$ the given expression, $\left( \array{ n\\n-2 } \right)$ evaluates to \begin{array}{l}\require{cancel} =\dfrac{n!}{(n-2)!(n-(n-2))!} \\\\= \dfrac{n(n-1)(n-2)!}{(n-2)!(n-n+2)!} \\\\= \dfrac{n(n-1)\cancel{(n-2)!}}{\cancel{(n-2)!}2!} \\\\= \dfrac{n(n-1)}{2(1)} \\\\= \dfrac{n(n-1)}{2} \end{array}