Combinations With Repetition Calculator
Multiset counting — donuts, dice and stars and bars.
Enter your values
ⓘ Live results
Results
- Combinations with repetition
- 35
- Combinations without repetition
- 10
- Permutations with repetition
- 125
- Permutations without repetition
- 60
- Stars and bars setup
- 3 stars and 4 bars
Quick answer
Choosing k items from n types with repetition allowed gives C(n + k − 1, k) possibilities — the stars and bars result.
C(n + k − 1, k)
How to use the Combinations With Repetition Calculator
- 1Enter how many distinct types you can choose from.
- 2Enter how many items you are picking.
- 3Read the repetition-allowed count, with the three other counting rules for comparison.
Worked example
Using the values the calculator loads with:
Inputs
- Number of types n5
- Items chosen k3
Results
- Combinations with repetition35
- Combinations without repetition10
- Permutations with repetition125
- Permutations without repetition60
- Stars and bars setup3 stars and 4 bars
Frequently asked questions
What is the classic example?
Choosing 3 donuts from 5 flavours when you can repeat flavours: C(7, 3) = 35 different boxes.
Why is it called stars and bars?
Picture k stars split into n groups by n − 1 bars; every arrangement of stars and bars is one valid selection.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.