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Question 290011
JEE Mathematics · Hard

Permutations and Combinations: Derangement MCQ

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DerangementHardQuestion 290011

Question

The number of ways 3 letters can be placed in 3 envelopes such that NO letter is in its correct envelope (derangement D₃) is:
  1. A
    2
    Correct
  2. B
    1
  3. C
    3
  4. D
    6

Correct answer

2

Explanation

Derangement formula: Dₙ = n!(1 − 1/1! + 1/2! − 1/3! + ...). D₃ = 3!(1 − 1 + 1/2 − 1/6) = 6(1/3) = 2.

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