Factorial
Etymology
From “factor” (Latin, “one who does,” from facere, to do), because a factorial multiplies successive factors. The word and the notation “n!” were introduced by the French mathematician Christian Kramp in 1808.
noun · /fak-TOR-ee-uhl/
The product of all whole numbers up to a given one, written with an exclamation mark, so 5! is 120.
What it names
It shows how fast the number of possible arrangements explodes as items are added — faster than almost any intuition allows.
Example
A deck of 52 cards can be ordered in 52 factorial ways — a number so vast that any well-shuffled deck has almost certainly never existed before.
Related idea
Factorials power permutation and combination counts and drive combinatorial explosion — the reason problems that look small become computationally hopeless as they scale.