A combination of a set of distinct object is an unordered arrangement of these objects.

For a set of \(n\) items, there is only one possible combination.


To choose \(k\) elements from a wider group on \(n\) a k-combination may be used.

For two integers \(n, k\) where \(0 \leq k \leq n\) possible combinations are: \[ C(n,k) = \frac{n!}{k!(n-k)!} \] This is also expressed as the Binomial coefficient \[ n \choose k \]


A k-combination with repetitions, or k-multicombination provide the number of multisets of length \(k\) on \(n\) symbols.

\[ \left(\!\! {n \choose k} \!\!\right) = {n + k - 1 \choose k} = \frac{(n+k-1)!}{k!(n-1)!} \]