Understand the subject
What is a combination?
A <strong>combination</strong> is a selection where membership matters but order does not. Choosing A then B is the same group as choosing B then A.
Use it for committees, hands, teams, and any unordered selection without repetition.
See the structure
One group, many orderings
ABCACBBACBCACABCBAone group
Worked example
Check the rule with a small case
Choose 3 people from 10: C(10,3) = 120 committees.
Interpret with care
Choose the right counting model
If first, second, and third roles differ, use a permutation instead.
Use the Permutation & Combination Generator when a small case needs to be inspected rather than only counted.
Quick guide
How to use this calculator
- Enter the total number of distinct objects n.
- Enter the number selected r.
- Read nCr, also called the binomial coefficient or n choose r.
Calculation method
Remove the ordering of each selection
Start from ordered selections and divide by the r! orders of each chosen group.
Worked example
Choose three from ten
A three-person committee chosen from ten people has 120 possible memberships.
C(10,3) = 10!/(3!7!) = 120
Supported inputs
Precision and limits
Discrete domain
Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.
Exact integers
Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.
