A familiar situation
Count team selections when membership matters, or assign distinct roles when order matters.
How to use this calculator
- Enter available items n, items selected r, count.
- Select Calculate to see the answer and its breakdown.
- Keep a scenario, change an input and compare the results.
Use consistent units and check the assumptions below before applying the result.
How permutation and combination is calculated
Permutation P(n,r)=n!/(n−r)!; combination C(n,r)=n!/[r!(n−r)!]. The calculation uses exact BigInt arithmetic before rendering the count. Selecting a president and vice president from 5 people gives P(5,2)=20 ordered assignments; choosing 2 committee members gives C(5,2)=10.
P(n,r)=n!/(n−r)!; C(n,r)=n!/[r!(n−r)!].Selecting a president and vice president from 5 people gives P(5,2)=20 ordered assignments; choosing 2 committee members gives C(5,2)=10.
Assumptions & useful context
The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.
Frequently asked questions
What is the difference between the modes?
Permutations distinguish different orders; combinations treat the same selected group as one outcome.
Can r exceed n?
No, a selection cannot contain more distinct items than are available.