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.

## k-combinations

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
\[
n \choose k
\]

## k-multicombination

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

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