Combination With Repetition Calculator

Work out combination with repetition instantly with clear inputs, formula shown and shareable results.

About Combination With Repetition Calculator

Choosing r items from n types with repetition allowed and order ignored is counted by stars and bars: C(n + r − 1, r). Each selection corresponds to placing r stars among n − 1 dividers.

Formulas

With repetition

C(n + r − 1, r)

Without repetition

C(n, r)

Worked example

With the default values below, Combination With Repetition Calculator returns Multisets (repeats allowed) of 35. Change any input above and every figure here is recalculated in your browser.

Inputs used

Types availableaccepts 1–200: 5
Items to chooseaccepts 0–200: 3

Results

Multisets (repeats allowed): 35
Plain combinations: 10
Stars and bars form: C(7, 3)
Extra selections allowed by repetition: 25

Step by step

1Values used
2With repetition
3Without repetition
4Multisets (repeats allowed)= 35
5Plain combinations= 10
6Stars and bars form= C(7, 3)
7Extra selections allowed by repetition= 25

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How many ways to pick 3 doughnuts from 5 kinds?

C(7, 3) = 35 if repeats are allowed, against only C(5, 3) = 10 if all must differ.

Why 'stars and bars'?

Represent the choice as r stars separated by n − 1 bars; every arrangement of those symbols is one multiset.