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Factorials are used in combinatorial mathematics, which is a fancy term for a branch of mathematics that's used to answer questions like "how many different ways are there to arrange N items?" (Answer: N!) It turns out that using the formulas developed by combinatorial mathematics, the term 0! occasionally turns up, and in order to obtain the correct answer it's necessary to replace 0! with 1. Most obviously, there's no other way to arrange a "set" of zero items than to have ... um ... zero items, so the number of ways zero items can be arranged is 1, therefore 0! = 1.

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Q: Why is factorial of 0 is 1?
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