Combinatorics (Fall 2010)/Basic enumeration

The twelvfold way

Elements of [math]\displaystyle{ N }[/math]	Elements of [math]\displaystyle{ M }[/math]	Any [math]\displaystyle{ f }[/math]	Injective (1-1) [math]\displaystyle{ f }[/math]	Surjective (on-to) [math]\displaystyle{ f }[/math]
distinguishable	distinguishable	[math]\displaystyle{ m^n }[/math]
indistinguishable	distinguishable		[math]\displaystyle{ {m\choose n} }[/math]
distinguishable	indistinguishable
indistinguishable	indistinguishable