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
Worth solving first
- Arranging MISSISSIPPI 3.0/10
- Trailing Zeros 3.0/10
- Tiling with Dominoes 3.0/10
Source: The 'probleme des rencontres', posed by Pierre Remond de Montmort (1708). Statement written for AxiomIQ.