Combinatorics is the branch of mathematics concerned with Counting, Combinations and Permutations of Sets.
For choosing \(k\) items from a set of \(n\).
| Order matters (Permutations) | Order does not matter (Combinations) | |
|---|---|---|
| Without repetition | \(\frac{n!}{(n-k)!}\) | \(\frac{n!}{k!(n-k)!}\) |
| With repetition | \(n^k\) | \(\frac{(k+n-1)!}{k!(n-1)!}\) |