CALCULATE WITH CONFIDENCE

Counting, Permutations & Combinations

Combinations with Repetition Calculator

Count unordered selections when each object type may be chosen repeatedly.

Counting & Combinatorics

Choose objects with repetition

Order ignored · repeats allowed
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Exact combinations

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Understand the subject

What is a combination with repetition?

This counts unordered selections when a type may appear more than once. A scoop of vanilla followed by chocolate is the same choice as chocolate followed by vanilla.

Use it for multisets such as flavor selections, inventory mixes, or counts by category.

The relationship

The counting rule

See the structure

Repeated types, not repeated order

Worked example

Check the rule with a small case

Four scoops from 3 flavors: C(3+4−1,4) = C(6,4) = 15.

Interpret with care

Choose the right counting model

The objects selected are identical within a type. Ordered sequences use permutations with repetition.

Use the Permutation & Combination Generator when a small case needs to be inspected rather than only counted.

Quick guide

How to use this calculator

  1. Enter the number of available object types n.
  2. Enter the selection size r.
  3. Read the exact number of multisets.

Calculation method

Use the multichoose formula

Choosing r objects from n types with repetition and without order is equivalent to a stars-and-bars arrangement.

Worked example

Choose four scoops from three flavors

Flavors may repeat and scoop order is ignored.

C(3+4−1,4) = C(6,4) = 15

Supported inputs

Precision and limits

Discrete domain

Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.

Exact integers

Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.