Derangements
n letters are placed randomly into n addressed envelopes, one per envelope. As n approaches infinity, what does the probability that no letter ends up in its correct envelope converge to? Express as a fraction or decimal rounded to 4 decimal places.
Related problems & prerequisites
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Source: The 'probleme des rencontres', posed by Pierre Remond de Montmort (1708). Statement written for AxiomIQ.