Factorial Calculator
Calculate the factorial of a number (n!). Also shows permutations and combinations with a second input.
Factorial N
3,628,800
Formule
## 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.
Exemple Résolu
Calculate 10!, P(10,3), and C(10,3).
- 0110! = 3,628,800
- 02P(10,3) = 10!/7! = 10×9×8 = 720
- 03C(10,3) = 720/3! = 720/6 = 120
Questions Fréquentes
What is a factorial?
n factorial (n!) is the product of all positive integers from 1 to n. For example, 5! = 120. By convention, 0! = 1.
What is the difference between permutations and combinations?
Permutations count ordered arrangements (ABC is different from BCA). Combinations count unordered selections (ABC is the same as BCA).
Why does 0! equal 1?
By convention and to make formulas work consistently. There is exactly one way to arrange zero objects: do nothing.
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