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Question

The probability that two randomly selected subsets of the set {1,2,3,4,5} have exactly two elements in their intersection, is 
  1. 13529
  2. 6528
  3. 6527
  4. 3527


Solution

The correct option is A 13529
Let A and B be two subsets.
For each x{1,2,3,4,5}, there are four possibilities :
xAB, xAB, xAB, xAB
So, the number of elements in sample space =45
Required probability
=5C2×3345
=10×27210=13529

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