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.