Factorial Calculator — Formula
## Factorial, Permutations, and Combinations
### Factorial
**n! = n × (n-1) × (n-2) × ... × 2 × 1**
0! = 1 by convention.
### Permutations (order matters)
**P(n, r) = n! / (n-r)!**
Number of ways to arrange r items from n distinct items.
### Combinations (order doesn't matter)
**C(n, r) = n! / (r! × (n-r)!)**
Number of ways to choose r items from n without regard to order.
### Factorial
**n! = n × (n-1) × (n-2) × ... × 2 × 1**
0! = 1 by convention.
### Permutations (order matters)
**P(n, r) = n! / (n-r)!**
Number of ways to arrange r items from n distinct items.
### Combinations (order doesn't matter)
**C(n, r) = n! / (r! × (n-r)!)**
Number of ways to choose r items from n without regard to order.
Esempio Risolto
Calculate 10!, P(10,3), and C(10,3).
- 10! = 3,628,800
- P(10,3) = 10!/7! = 10×9×8 = 720
- C(10,3) = 720/3! = 720/6 = 120