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Problem #105 MEDIUM

The Number e Hiding in a Card Deck

Paradox Combinatorics Math

Problem Statement

A standard deck of 52 cards is shuffled randomly. What is the probability that not a single card ends up in its original position — every card is displaced? Now suppose you shuffle n cards instead of 52. As n grows large, the probability approaches a famous constant. What is that constant, and why does a geometry-free problem produce a result involving e?

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