Binomial Coefficients

Binomial coefficients in discrete mathematics are denoted \({n \choose k}\), where we say \(n\) choose \(k.\) The variable, \(n,\) is usually known as the upper index while the variable, \(k,\) is known as the lower index. Binomial coefficients are the same amount of combinations of \(k\) items that can be chosen from a set of \(n\) items where order does not matter. Therefore, \({n \choose k}\) gives the \(k\) subsets that are possible out of \(n\) total items. When looking further into binomial coefficients, we notice that the values are non-negative. 
The reason why these numbers are called binomial coefficients is because the numbers themselves appear as coefficients in the expansion of a binomial, \(\left(1+d\right)^n,\) in growing powers of \(d.\)