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# Combinations

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.

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