Combinations
Calculator
Results
- Number of combinations
- 792
- Factorial of n
- 479,001,600
Statistical results
| Number of combinations | 792 |
| Factorial of n | 479,001,600 |
formula-map diagram
- Number of combinations
- 792
- Factorial of n
- 479,001,600
Statistical relationship
Formula
C(n, k) = n! / (k! × (n − k)!)= 792
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What do combinations count, and how is that different from permutations?+
Combinations count the number of ways to choose a subset of items where order doesn't matter, like picking a 3-person committee from 10 people. Permutations count the same kind of selection but where order does matter, such as assigning 1st, 2nd, and 3rd place.
What is the formula for combinations?+
The formula is C(n,r) = n! / (r! × (n−r)!), where n is the total number of items and r is the number chosen. Dividing by r! is what removes the order-dependence that a straight permutation count would include.
Why does choosing r items give the same count as choosing n−r items?+
Choosing which r items to include is equivalent to choosing which n−r items to leave out, so C(n,r) always equals C(n, n−r). For example, choosing 3 people out of 10 to include is the same count as choosing 7 people out of 10 to exclude.
What does C(n,0) or C(n,n) equal, and why?+
Both equal exactly 1. There's exactly one way to choose nothing from a group (the empty set) and exactly one way to choose the entire group, since there's no variation possible in either case.
Where do combinations show up outside of pure math problems?+
They're used to calculate lottery odds, poker hand probabilities, and how many possible test question subsets or group pairings exist. Any scenario where you're selecting a group without regard to the order of selection is a combinations problem.