← Math & statistics

nCr & nPr Calculator (Permutations & Combinations)

Enter n and r to compute permutations, combinations, and factorial values with BigInt exact results, scientific-notation approximations, shareable URLs, and optional teaching prompts.

Keep teacher mode on to surface symmetry hints and definitions, or switch to Approx whenever the exact value would exceed the safe BigInt workload (about n = 10,000).

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Mode
Precision

Results

Exact value:
Digits:
Scientific notation:

Step log

Steps are hidden. Turn on “Show steps” to view them.

    FAQ

    What is the difference between permutations and combinations?

    Permutations treat the order of selection as unique (AB ≠ BA). Combinations treat those as the same outcome, counting only distinct subsets.

    When should I switch between Exact and Approx?

    Use Exact for values within the BigInt range (up to about n = 10,000 with k ≤ 5,000). Switch to Approx when the exact integer would be too large; you will still see the digit count and an accurate scientific notation.

    What should I enter first for nCr or nPr?

    Choose combination or permutation first, then enter n and r. Confirm whether order matters and whether repetition is allowed before using the count.

    Why can nCr or nPr results differ from nearby tools?

    Differences usually come from order, repetition, n, r, and whether the task is selection or arrangement. Match those assumptions before comparing this result with another CalcBE page, spreadsheet, or external tool.

    How should I judge the reliability of the result?

    Use the displayed result as reliable for the stated order, repetition, n, r, and whether the task is selection or arrangement. For official reporting, regulated work, or purchasing decisions, verify the inputs against the source document or provider rule you must follow.

    How to use nCr and nPr Calculator effectively

    What this page is for

    Use this page to count combinations and permutations from n and r. Start by deciding whether order matters.

    Input checks

    Check whether repetition is allowed and whether n and r are whole nonnegative counts. Invalid counts should not be forced into the formula.

    Workflow

    A practical sequence is to compute combinations for selection problems and permutations for arrangement problems, then compare only if the scenario permits both.

    Common mistakes

    Avoid using permutation counts for unordered selections. That overcounts outcomes by treating order as meaningful.

    How to read the result

    Interpret the result as a count of possible outcomes under the stated assumptions, not as a probability unless each outcome is equally likely and a denominator is defined.

    Related

    How it’s calculated

    • Uses factorial identities: nCr = n!/(r!(n−r)!) and nPr = n!/(n−r)! with big‑integer safeguards.
    • Out‑of‑range inputs are rejected; results are formatted with grouping for readability.
    • The shareable URL stores n and r so you can rerun the same case.