Quick Basics of Enumerative Combinatorics
While going through past notebooks, I came across a table I’d compiled which covered basic enumerative combinatorics.
| choose \(r\) from \(n\) | ordered | unordered |
|---|---|---|
| no repititions | \(\frac{n!}{(n-r)!}\) | \({n \choose r}\) |
| repetitions | \(n^r\) | \({n+r-1 \choose r}\) |
Note that \({n \choose r} = \frac{n!}{r!(n-r)!}\) and is pronounced “\(n\) choose \(r\)”.
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