Question

ol: Total number of binary operations on ( A=12^{12^{2}} ) and number of commutative binary operations on A is ( 12^{12}left(frac{12+1}{2}right) )
Required probability ( =frac{12^{12}left(frac{12+1}{2}right)}{12^{12^{2}}}=frac{1}{12^{66}} )

# W.E.35:- A binary operation is chosen at random from the set of binary operations on a set A consisting 12 elements. The probability that the binary operation is commutative is

Solution