Factorial of n (written n!) is the product of all positive integers from 1 to n: n! = n × (n−1) × ... × 2 × 1. Factorials appear in combinations, permutations, probability, and Taylor series expansions.
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Pro Tip
Stirling's approximation: n! ≈ √(2πn) × (n/e)ⁿ. For large n, this is very accurate. For n=10: exact = 3,628,800; Stirling gives 3,598,696 (0.83% error).
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Did You Know?
The number of ways to shuffle a standard 52-card deck is 52! ≈ 8 × 10⁶⁷. This number is so large that every time you shuffle a deck, you are almost certainly creating an ordering that has never existed before in human history.
References
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