The probability that two randomly selected subsets of the set  1,2,3,4,5 have exactly two elements in their intersection, is

Let S = {1, 2, 3, 4, 5}    Suppose that   A ,.   B  are any two subsets of S For each element of S has four choices, it may belongs to A, or it may belongs to B, or it may belongs both A and B or it may does not belongs to both A and B So total number of cases is 45           Let two elements be selected in C(5,2) ways .Remaining elements are 3. each element has choice, it may lie in A or in B or not in both A and Bhence, the total favorable cases to the event is C(5,2) 33 ∴PE=  5C2×3345=27×529=13529