binary operation

Question

out of all binary operation possible on a set with 3 element, a binary operation is selected at random.find the probability that chosen binary operation is being  non commutative .

Answer 1

total no of binary operation $n^{n^{2}}$

no of commutative binary operation $n^{((n^{2}+n)/2)}$

no of non commutative binary operation $n^{n^{2}}$  $-$$n^{((n^{2}+n)/2)}$

probability of non commutative $n^{n^{2}}$$-$$n^{((n^{2}+n)/2)}$$/$$n^{n^{2}}$