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Four letters are to be placed into four addressed envelopes. In how many ways can the letters be arranged so that none of them goes into its own correct envelope?
- 9
- 4
- 5
- 12
Correct answer: 9
Solution
The number of arrangements with no letter in its correct envelope is the derangement D4 = 4!(1 - 1/1! + 1/2! - 1/3! + 1/4!) = 24(1 - 1 + 1/2 - 1/6 + 1/24) = 9.
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