Derangements and the number e
If a teacher randomly hands back 20 homework assignments to the 20 students who wrote them, what is the probability that none of the students receives their own homework back? The answer turns out to be about 0.368, or 36.8%. Remarkably, this number is very close to 1/e, where the number e is the base of the natural logarithm (approximately 2.718). The …
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