Factorials (n!) — the cascade multiplier

The factorial of n (written n!) = the product of all whole numbers from 1 up to n.

• 1! = 1
• 2! = 1·2 = 2
• 3! = 1·2·3 = 6
• 4! = 1·2·3·4 = 24
• 5! = 120, 6! = 720, 7! = 5,040

Each next factorial = (previous) × n. So sequence grows as: 1, 2, 6, 24, 120, 720, 5040, 40320, …

Factorials count arrangements. 3 friends can line up in 3! = 6 orders. A 52-card deck can be shuffled in 52! (≈ 8 × 10⁶⁷) ways — astronomical.