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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