Factorial Calculator
Calculate the factorial of a number (n!). Also shows permutations and combinations with a second input.
Factorial N
3,628,800
सूत्र
## 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.
हल किया गया उदाहरण
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
अक्सर पूछे जाने वाले प्रश्न
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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