factorial

`n!` is `1 × 2 × 3 × … × n`. It counts orderings: `n!` is the number of distinct ways to arrange n items in a line. `5! = 120`. `52!` (the number of distinct shuffles of a deck) is a 68-digit number. Grows faster than any exponential `aⁿ`, which is why `log(n!)` and Stirling's approximation matter.