मुफ्त क्रमगुणन कैलकुलेटर
किसी संख्या का क्रमगुणन (n!) निकालें। संख्या दर्ज करें और फैक्टोरियल तुरंत गणना करें।
Factorial N
3,628,800
Factorial R6
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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