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JEE Main 202124 FebruaryEvening Shift
Exam
JEE Main
Year
2021
Date
24 February
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2021 · 24 February · Evening Shift · Mathematics · Probability

The probability that two randomly selected subsets of the set 1, 2,...

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

Options

  1. A6528\dfrac{65}{{2}^{8}}
  2. B6527\dfrac{65}{{2}^{7}}
  3. C3527\dfrac{35}{{2}^{7}}
  4. D13529\dfrac{135}{{2}^{9}}

Correct answer

D. 13529\dfrac{135}{{2}^{9}}

Step-by-step solution

Total subsets=25=32= {2}^{5} = 32

Probability=C25×3332×32=10×27210=13529= \dfrac{C2 5 \times {3}^{3}}{32 \times 32} = \dfrac{10 \times 27}{{2}^{10}} = \dfrac{135}{{2}^{9}}

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