JEE Main 2021 (Online) 24th February Evening ShiftQuestion 1
The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is :
Probability
Solution
Each element is in $(A,B)$ in 4 ways (none, only A, only B, both), exactly 2 elements in both: $\binom52\cdot3^3=270$ out of $4^5=1024$. $P=\frac{270}{1024}=\frac{135}{2^9}$. Option (C).