When to use this
Use this formula when the question matches this rule set
Math homework, symbolic notation, and binomial theorem references.
What this result means
Interpret the output, not just the number
The binomial coefficient equals the number of unordered selections of r items from n distinct items without repetition.
Formula: C(n, r) = nCr = n! / r!(n - r)!
Calculator inputs
Know what to enter in each field
Match the wording in the question to these fields before you interpret the result.
n - total items
This is the full number of distinct items available.
What to enter: Enter the total size of the set.
How to use it: This page is notation-focused, but the meaning matches combinations without repetition.
Example: For C(12, 5), enter 12.
r - items chosen
This is the subset size.
What to enter: Enter how many items are being chosen.
How to use it: Use the lower argument from nCr or C(n, r).
Example: For C(12, 5), enter 5.
Worked examples
Quick checks with realistic inputs
Symbolic notation
Evaluate C(10, 3) directly.
The binomial coefficient C(10, 3) is 120.
Load this example into the calculatorBinomial theorem term count
Use nCr to evaluate coefficients like C(12, 5).
The binomial coefficient C(12, 5) is 792.
Load this example into the calculator