Combinations With Repetition Calculator
Multiset counting — donuts, dice and stars and bars.
Enter your values
Enter the number of types n you are working with.
Enter the items chosen k you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Multiset counting — donuts, dice and stars and bars. |
|---|---|
| Category | Math |
| Inputs needed | Number of types n, Items chosen k |
| Main output | Combinations with repetition |
| Formula | C(n + k − 1, k) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Number of types n
- Enter the number of types n you are working with.
- Items chosen k
- Enter the items chosen k you are working with.
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.
What do I need to enter into the Combinations With Repetition Calculator?
Just 2 values: number of types n, items chosen k. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Combinations With Repetition Calculator work out the answer?
Choosing k items from n types with repetition allowed gives C(n + k − 1, k) possibilities — the stars and bars result. It applies the formula C(n + k − 1, k) and shows the working so you can check each step by hand.
Is the Combinations With Repetition Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.