If |X| = n > 0, there are 1C1(adsbygoogle = window.adsbygoogle || []).push({}); ^{nC1}2C1^{nC2}...nC1^{nCn}many choice functions from (power set of X minus empty set) P(X)\{{}} to X?

Just curious. I'm jumping ahead a bit, but that makes sense to me. Is it correct? Is it much more difficult to understand when X is infinite?

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# How many choice functions?

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