JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Probability

The probability that two randomly selected subsets of the set

{1, 2, 3, 4, 5}

have exactly two elements in their intersection is:

Answer: (C)

Solution

Each subset is chosen from

2^{5}

possibilities, so there are

2^{10}

equally likely ordered pairs. The two elements lying in both subsets can be chosen in

(2 5) = 10

ways, and each of the other three elements must then belong to the first subset only, the second only, or neither, which is

3

choices each and

3^{3} = 27

in all. The probability is

\frac{10 \cdot 27}{2 ^{10}} = \frac{270}{1024} = \frac{135}{512},

so the required probability is

\frac{135}{2 ^{9}}

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Single correct option