Combination Calculator
Count unordered selections nCr with exact big-integer results for large inputs.
Combination Calculator
Count unordered selections nCr with exact big-integer results for large inputs.
How to use the Combination Calculator
- Enter n (total items).
- Enter r (items to choose).
- Click Calculate.
Formula
C(n, r) = n! / (r! × (n − r)!)
Example
C(10, 3) = 10! / (3! × 7!) = 120
Step-by-step calculation
- C(10,3) = (10 × 9 × 8) / (3 × 2 × 1) = 720 / 6 = 120.
- 120 unique groups of 3.
Real-world uses
- Team selection possibilities.
- Card hand probabilities.
- Lottery odds calculation.
Common mistakes
- Confusing combinations with permutations.
- Not accounting for the fact that order does not matter.
- Entering r > n.
Frequently asked questions
What is the difference from permutations?
Combinations ignore order (ABC = BCA). Permutations count each arrangement separately.
Is C(n, r) the same as C(n, n−r)?
Yes. Choosing 3 from 10 is the same as choosing 7 to leave out.
How large can the numbers be?
Up to 1,000,000 for n and r. Results use exact big-integer arithmetic.