FACTORIAL

The factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n: n! = n ⋅ (n - 1) ⋅ (n - 2) ⋅ (n - 3)⋅...⋅3⋅2⋅1

The value of 0! is 1, according to the convention for an empty product.

The factorial counts the possible distinct sequences (the permutations) of n distinct objects.

Factorial: n ∈ ℕ, n! = {1 (n=0); 1⋅2⋅3⋅n (n≠0)}

3! = 1⋅2⋅3 = 6

5! = 1⋅2⋅3⋅4⋅5 = 120

n! is the number of possible orders of n objects.

3! = 6; abc, acb, bac, bca, cab, cba = 6 possible distinct sequences (permutations).

In general, n objects can be sorted into n! different ways.