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Factorial
The factorial of a whole number n, written as n!,^{[1]} is found by multiplying n by all the whole numbers less than it. For example, the factorial of 4 is 24, because 4 × 3 × 2 × 1 = 24. Hence one can write 4! = 24. For some technical reasons, 0! is equal to 1.^{[2]}
Factorial can be used to find out how many possible ways there are to arrange n objects.^{[2]}
For example, if there are 3 letters (A, B, and C), they can be arranged as ABC, ACB, BAC, BCA, CAB, and CBA. That would be 6 choices because A can be put in 3 different places, B has 2 choices left after A is placed, and C has only one choice left after A and B have been placed. In other words, 3×2×1 = 6 choices.
The factorial function is a good example of recursion (doing things over and over), as 3! can be written as 3×(2!), which can be written as 3×2×(1!) and finally as 3×2×1×(0!). N! can therefore also be defined as N×(N1)!,^{[3]} with 0! = 1.^{[2]}
The factorial function grows very fast. There are 10! = 3,628,800 ways to arrange 10 items.^{[3]}
Notes
n! is not defined for negative numbers. However, the related gamma function is defined over the real and complex numbers (but the integers it is defined over are positive).^{[2]}
Related pages
References
 ↑ "Compendium of Mathematical Symbols" (in enUS). 20200301. https://mathvault.ca/hub/highermath/mathsymbols/.
 ↑ ^{2.0} ^{2.1} ^{2.2} ^{2.3} Weisstein, Eric W.. "Factorial" (in en). https://mathworld.wolfram.com/Factorial.html.
 ↑ ^{3.0} ^{3.1} "Factorial Function !". https://www.mathsisfun.com/numbers/factorial.html.
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