# combination

A combination is a sub-selection of elements from a given set of elements. Typically we are concerned to count the number of possible combinations, that is, the number of possible ways to select a given number of elements from a set of some given size.

The number of ways of selecting $$r$$ elements from a set of $$n$$ elements is generally denoted by $$\left(\begin{array}{c}n \\ r \end{array} \right)$$ and described as ‘$$n$$ choose $$r$$.’ It is equal to the binomial coefficient and may be calculated according to the formula

$\left(\begin{array}{c}n \\ r \end{array} \right) = \frac{n!}{r!(n-r)!}$

It is also sometimes denoted by $$\mbox{}_nC_r$$.