# 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