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If n letters, each with its own correctly addressed envelope, are inserted into the envelopes in a completely random manner, what is the probability that all n letters end up in their proper envelopes?
- 1/1! + 1/2! + 1/3! + 1/4! +... + (-1)ⁿ 1/n!
- 1/2! + 1/3! + 1/4! + 1/5! +... + 1/n!
- 1/2! - 1/3! + 1/4! - 1/5! +... + (-1)ⁿ 1/n!
- None of these
Correct answer: None of these
Solution
All n letters in correct envelopes corresponds to a single arrangement (the identity), so the probability is 1/n!. This value is not among the listed series, so the answer is 'None of these'.
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