Result
Enter values and select Calculate.
Formula and method
For 0 ≤ r ≤ n, C(n,r) = n! / (r!(n−r)!). The engine uses k = min(r,n−r) and exact iterative BigInt multiplication and division, avoiding floating-point factorial division.
Worked example
Choosing 3 people from 10 gives C(10,3) = 120. Because order does not matter, C(10,3) also equals C(10,7).
Inputs and boundaries
- n and r must be nonnegative integers, with r no greater than n.
- The calculation is without repetition.
- Inputs are limited to 10,000 to keep very large results responsive.
- The full exact integer is returned; no floating-point precision is lost.
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