Statistics

Combination Calculator

Computes nCr, the number of unordered combinations when choosing r items from n where order does not matter. Enter total items and chosen items to get the count of possible selections.

What this calculator does

The Combination Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Computes nCr, the number of unordered combinations when choosing r items from n where order does not matter. Enter total items and chosen items to get the count of possible selections. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.

Combination Calculator

Result

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Combinations nCr

About Combination Calculator

This combination calculator finds nCr, the number of ways to pick r items from a set of n when the order of selection does not matter. It uses nCr = n! ÷ (r! × (n − r)!).

Enter the total number of items and how many you are choosing to see the total count of distinct groups.

Formula & Mathematical Calculation

Combinations nCr = f(Total items (n), Chosen items (r))

Calculated according to standard stats formulas implemented in the calculator core.

Calculation Example

Choosing 3 items from 10: nCr = 10! ÷ (3! × 7!) = 3,628,800 ÷ (6 × 5,040) = 120. The calculator shows 120 combinations.

Key Benefits

  • Returns the exact count of unordered selections for any valid n and r
  • Handles large factorials using a log-gamma method that avoids overflow
  • Confirms in one step that order does not matter, unlike permutations

How to Use this Calculator

  1. Enter total items (n)
    Type the total number of items in the set into the Total items (n) field, for example 10.
  2. Enter chosen items (r)
    Type how many items you are selecting into the Chosen items (r) field, for example 3. It must not exceed n.
  3. Calculate
    Select Calculate to see the number of combinations (nCr) and a plain-language summary.

Assumptions & Limitations

What the calculation assumes

  • Every value you enter is treated as an exact, known amount.
  • Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
  • Results use standard published formulas and account only for the values entered above.
  • Rounding is applied for display; the underlying calculation uses your full precision.
  • Results are returned in the same units you enter, unless the tool states the output unit.

What it does not cover

  • Combination Calculator produces a calculated result for reference and learning, not a certified or official measurement.
  • Real-world outcomes differ when tolerances, rounding rules or local standards apply.
  • Definitions and standards vary by region and change over time; verify the convention that applies to your case.
  • Figures are only as accurate as the inputs you supply — check them before acting on the result.
  • For work where the result carries real consequences, confirm it against an authoritative source.

Frequently Asked Questions

It uses nCr = n! / (r! * (n - r)!), computed with a log-gamma routine so large values stay accurate.

A combination counts selections where order does not matter, so choosing A then B is the same as B then A. A permutation counts ordered arrangements.

The calculator shows an error asking you to lower r, because you cannot choose more items than the set contains.

Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.