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NDA 2019 Maths · Mathematics · Probability · medium

Three letters are placed at random into three addressed envelopes, one in each. The probability that none of the letters goes into its own envelope is

Single correct option

Three letters are placed at random into three addressed envelopes, one in each. The probability that none of the letters goes into its own envelope is
  1. A. 16\frac16
  2. B. 12\frac12
  3. C. 23\frac23
  4. D. 13\frac13
Show answer and solution

Answer: (D) 13\frac13

There are 3!=63!=6 arrangements, and those with no letter in its own envelope are the derangements: 22 of them (the two cyclic shifts). So the probability is 26=13\frac26=\frac13. The value 16\frac16 is the probability that all three are correct.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake