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

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

$\frac{65}{2^{8}}$

$\frac{35}{2^{7}}$

$\frac{65}{2^{7}}$

answer is D.

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Detailed Solution

given set { 1, 2, 3, 4, 5 } no of sub sets $2^{5} = 32$

two are selected at random

P(an element is common for both subsets)=1/4

P(an element is not common for both subsets)=3/4

E=two sets having two elements common

$P (E) = {}^{5}{C_{2} \times {(\frac{1}{4})}^{2}} \times {(\frac{3}{4})}^{3} = \frac{10 \times 27}{2^{10}} = \frac{135}{2^{9}}$

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