QJEEM21Mab6c5: JEE Main 2021 Mathematics - Class 12 JEEM21Mab6c5 Solution: The probability that two randomly selected subsets of the set…

Given, set P = {1, 2, 3, 4, 5}

Let the two subsets be A and B

Then, n (A $\cap$ B) = 2 (as given in question)

We can choose two elements from set P in ⁵C₂ ways.

After choosing two common elements for set A and B, each of remaining three elements from set P have three choice (1) It can go to set A (2) It can go to set B (3) It don't go to any sets it stays at set P.

$\therefore$ Total ways for the three elements = 3 $\times$ 3 $\times$ 3 = 3³

$\therefore$ Required probability = ${{{}^5{C_2} \times {3^3}} \over {\left( {{2^5}} \right)\left( {{2^5}} \right)}}$ = ${{{}^5{C_2} \times {3^3}} \over {{4^5}}} = {{10 \times 27} \over {{2^{10}}}} = {{135} \over {{2^9}}}$