Chapter 11 - Further Topics in Algebra - 11.4 The Binomial Theorem - 11.4 Exercises - Page 1045: 22

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

$\binom{n}{n-2}=\dfrac {n!}{\left( n-2\right) !\times \left( n-\left( n-2\right) \right) !}=\dfrac {n!}{\left( n-2\right) !\times 2!}=\dfrac {\left( n-2\right) !\times \left( n-1\right) \times n}{\left( n-2\right) !\times 1\times 2}=\dfrac {n\left( n-1\right) }{2}$