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KVPY2017MathematicsProbability

Suppose four balls labelled 1,2,3,4 are randomly placed in boxes B ₁, ~B ₂, ~B ₃, ~B ₄ . The probability that exactly one box is empty is

Options

  1. A8 256
  2. B9 16
  3. C27 256
  4. D9 64

Correct answer

B. 9 16

Step-by-step solution

required probability = ⁴ C ₁ 4 ! (1 !)² 2 ! 1 2 ! 3 ! 4⁴ = 9 16

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