Combinations Count
Calculator
Results
- Combinations C(n, r)
- 792
- Permutations P(n, r)
- 95,040
- Complement combinations C(n, n − r)
- 792
Results
| Combinations C(n, r) | 792 |
| Permutations P(n, r) | 95,040 |
| Complement combinations C(n, n − r) | 792 |
formula-map diagram
- Combinations C(n, r)
- 792
- Permutations P(n, r)
- 95,040
- Complement combinations C(n, n − r)
- 792
Formula map
Formula
C(n, r) = n! ÷ (r! × (n − r)!)= 792
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
More in Mathematics
See all →Frequently asked questions
What do n and r mean in C(n, r)?+
n is the total number of items, and r is how many you are choosing, without regard to order. C(n, r) counts how many distinct groups of r items can be formed from n total.
What is the formula?+
C(n, r) = n! / (r! × (n-r)!). It starts from the permutations formula and then divides by r! to remove the duplicate orderings of the same group.
How is this different from permutations?+
Combinations ignore order — choosing {A, B} is the same as choosing {B, A} — while permutations treat them as different. Combinations will always give an equal or smaller count than permutations for the same n and r.
Why is C(n, 0) always equal to 1?+
There is exactly one way to choose nothing — the empty set — regardless of how large n is, which is why C(n, 0) = 1 for any n.
Why is C(n, r) equal to C(n, n-r)?+
Choosing which r items to include is equivalent to choosing which (n-r) items to leave out, so both selections produce the same count — this symmetry is a useful sanity check on your result.