The probability that two randomly selected subsets of the set 1,2… - Vidyadip

MCQ

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

A
$\frac{65}{2^{7}}$
B
$\frac{65}{2^{8}}$
✓
$\frac{135}{2^{9}}$
D
$\frac{35}{2^{7}}$

✓

Answer

Correct option: C.

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

c
Total subsets $=2^{5}=32$

Probability $=\frac{{ }^{5} C _{2} \times 3^{3}}{32 \times 32}=\frac{10 \times 27}{12^{10}}=\frac{135}{2^{9}}$

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