Prove-that-number-of-commutative-binary-operations-on-a-set-having-n-elements-is-n-n-n-1-2-

Question Number 15302 by Tinkutara last updated on 10/Jun/17

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{number}\:\mathrm{of}\:\mathrm{commutative} \\ $$$$\mathrm{binary}\:\mathrm{operations}\:\mathrm{on}\:\mathrm{a}\:\mathrm{set}\:\mathrm{having}\:{n} \\ $$$$\mathrm{elements}\:\mathrm{is}\:{n}^{\frac{{n}\left({n}\:−\:\mathrm{1}\right)}{\mathrm{2}}} \:. \\ $$

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