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)”.
Written on January 28, 2014