Count unordered selections exactly with or without repetition. Use integer combinations for subsets and multisets without factorial overflow.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
Without repetition: C(n,r). With repetition: C(n+r−1,r). Order is ignored.
Assumptions and limits
Exact integer arithmetic. Limits: n and r up to 10,000; no ordered sequences or unequal selection weights. Multiset counts are not generally equally likely under repeated independent drawing.
Worked example
Choosing three distinct members from ten people gives C(10,3) = 120 unordered committees. Assigning three distinct roles would instead create 720 ordered assignments, which is not this tool’s output. If five types can repeat and three items are chosen without regard to order, C(5+3−1,3) = 35 multisets. Exact counting does not automatically make every counted outcome equally likely.
Worked reading and practical questions
- Choose a Subset or Arrange a Sequence? Decide Before Counting
- Combinations with Repetition: Types, Totals and Stars and Bars
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
Exact integer arithmetic. Limits: n and r up to 10,000; no ordered sequences or unequal selection weights. Multiset counts are not generally equally likely under repeated independent drawing.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.