Combination Calculator
Use this combination calculator when the selected group matters but its order does not. Calculate nCr without repetition or combinations with repetition using exact integer arithmetic.
How to use the Combination Calculator
- Enter the total number of available items n.
- Enter the number of items r to select.
- Choose whether repetition is allowed.
- Without repetition, the calculator uses n! divided by r! times (n − r)!.
- With repetition, it uses the standard multiset combination formula.
Examples
Choose 3 from 10
10C3 = 120. There are 120 different groups of 3 items selected from 10 when order does not matter.
Order does not matter
ABC and CBA represent the same combination because they contain the same selected items.
Combinations with repetition
When repeated selections are allowed, the calculator uses the multiset coefficient based on n and r.
Frequently asked questions
What is a combination?
A combination is a selection where order does not matter. Rearranging the same selected items does not create a new combination.
What does nCr mean?
nCr is the number of ways to choose r items from n distinct items when order does not matter and repetition is not allowed.
When should I use combinations instead of permutations?
Use combinations when only membership in the selected group matters. Use permutations when different orders are distinct outcomes.
Can combinations include repetition?
Yes. Combinations with repetition count selections where an item may appear more than once while order still does not matter.
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