Definition: Binomial Coefficients

Let \(X\) be a finite set with exactly \(n\) elements \((|X|=n)\). The number of possible combinations of size \(k\), \(0\le k\le n\) is called the binomial coefficient and denoted it by \[\binom nk.\] The symbol \(\binom nk\) is read "\(n\) choose \(k\)".