Exercise 999Combinatorics › Inclusion-exclusionL1Added 3 Nov 2026

Letters and envelopes

#IE#derangements#letters

Statement

Five letters are put randomly into five envelopes. What is the probability that no letter is in its correct envelope?

Hint

Derangements: $D_5/5!$ .

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Compute. $D_5=44$ , total $5!=120$ .

Probability. $44/120=11/30\approx0.3667$ .

Conclusion. Probability $=11/30$ .

Approximation. $D_n/n!\to1/e\approx0.368$ ; $11/30\approx0.367$ , close.