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Combinatorics

Combinatorics is the branch of mathematics concerned with Counting, Combinations and Permutations of Sets.

Formulas

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 \(n^k\) \(\frac{(k+n-1)!}{k!(n-1)!}\)