Derangement Probability with Envelopes - Quant Trader Interview Question
Difficulty: Hard
Category: Probability & Statistics
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: probability, asymptotics, derangement, limits
Problem Description
You are working as a quantitative analyst and encounter the following problem:
Imagine you have $N$ distinct letters and $N$ corresponding addressed envelopes. You randomly place each letter into an envelope. As $N$ approaches infinity, what is the probability that none of the letters are placed in the correct envelope?
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