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 $0\le k\le n$ possible combinations are: $$C(n,k)=\frac{n!}{k!(n-k)!}$$ This is also expressed as the Binomial coefficient $$(\genfrac{}{}{0ex}{}{n}{k})$$

k-multicombination

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

$$\left((\genfrac{}{}{0ex}{}{n}{k})\right)=(\genfrac{}{}{0ex}{}{n+k-1}{k})=\frac{(n+k-1)!}{k!(n-1)!}$$