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 \(r\)”.