Combination (nCr) Calculator
Calculate the number of ways to choose r items from a group of n when the order of selection doesn't matter.
Your results
Calculation breakdown
- Combination
- nCr = n! / (r! × (n − r)!)
Worked example
Choosing 3 people from a team of 10 for a project (where the order they're picked doesn't matter) gives 10C3 = 120 possible groups.
Assumptions
- Combinations count selections where order does not matter; use Permutation if order matters.
- Large n and r values are computed iteratively to avoid factorial overflow, but results above n ≈ 170 may lose precision.
How this calculator works
Enter the total number of items (n) and how many are chosen (r). The calculator returns nCr, the number of ways to select a group where the order of selection makes no difference.
Frequently asked questions
How is a combination different from a permutation?
A combination ignores the order of selection, while a permutation counts each different order as a separate outcome.
What does nCr mean?
nCr is read as 'n choose r' and represents the number of distinct groups of r items you can select from n items.
What if r is larger than n?
That's not a valid combination — you can't choose more items than exist in the group, so the calculator will show an error.