The probability that two randomly

Question:

The probability that two randomly selected subsets of the set $\backslash\{1,2,3,4,5 \backslash\}$ have exactly two elements in their intersection, is:

  1. (1) $\frac{65}{2^{7}}$

  2. (2) $\frac{135}{2^{9}}$

  3. (3) $\frac{65}{2^{8}}$

  4. (4) $\frac{35}{2^{7}}$


Correct Option: , 2

Solution:

Required probability

$=\frac{{ }^{5} C_{2} \times 3^{3}}{4^{5}}$

$=\frac{10 \times 27}{2^{10}}=\frac{135}{2^{9}}$

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