Combinations with Repetition Calculator
Count how many ways you can choose r items from n types when repeats are allowed and order does not matter. The tool applies the multiset formula C(n + r - 1, r) and shows the total as a whole number.
What this calculator does
The Combinations with Repetition Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Count how many ways you can choose r items from n types when repeats are allowed and order does not matter. The tool applies the multiset formula C(n + r - 1, r) and shows the total as a whole number. 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.
Result
About Combinations with Repetition Calculator
When you pick items and the same type can be chosen more than once, the count of distinct selections is a combination with repetition. Given n types and r items chosen, this calculator evaluates C(n + r − 1, r), the standard multiset formula, using a numerically stable binomial routine.
Enter a whole number of types (at least 1) and a whole number of items chosen (0 or more). The answer is displayed with thousands separators.
Formula & Mathematical Calculation
Combinations with repetition = f(Types of items (n), Items chosen (r))
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
With types n = 5 and items chosen r = 3:
- C(n + r − 1, r) = C(5 + 3 − 1, 3) = C(7, 3)
- C(7, 3) = 35
The Combinations with repetition box reads 35.
Key Benefits
- Applies the multiset formula C(n + r - 1, r) so repeats are counted correctly without double-counting orderings
- Uses a log-gamma based binomial routine that stays stable for larger n and r
- Formats the count with thousands separators for easy reading
- Validates that n is at least 1 and r is 0 or more; free and runs in the browser
How to Use this Calculator
-
Enter the number of types
Type how many distinct kinds of item you can choose from into Types of items (n); at least 1. -
Enter the number chosen
Type how many items you are selecting into Items chosen (r); 0 or more. -
Calculate
Press Calculate to read the total number of combinations with repetition.
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
- Combinations with Repetition 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
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.