The factorial

The factorial is the basic operation for counting the orderings of a set of objects.

Definition — Factorial

For $n\in\mathbb{N}$ one defines $n! = n\cdot (n-1)\cdot (n-2)\cdots 2\cdot 1$ with the convention $0! = 1$.

The number $n!$ counts how many different ways one can arrange $n$ distinct objects in a row: the first position can be filled in $n$ ways, the second in the $n-1$ remaining ones, and so on until the last. These orderings are called permutations of $n$ objects.

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Topics: Combinatorics
Concepts: Factorial · Permutations
Methods: Factorial permutations
Skills: Combinatorial calculus