Calculatrice de Factorielle Avancée Gratuite
Calculez les factorielles avec des fonctionnalités avancées. Obtenez n!, les doubles factorielles et la fonction gamma.
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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