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Combinations with Repetition Calculator

Online repetition combination: choose m items from n types without order, C(n+m−1,m).

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C(n+m−1,m)
Types
Count

📖 Tutorial | Repetition Comb

1. Definition
Choosing m items from n types with replacement, without order, gives C(n+m−1,m) by stars and bars.
2. Formula & Notation
n,mTypes, count
3. Properties & Laws
  • Repeats, unordered;
  • Stars and bars;
  • C(n+m−1,m)=C(n+m−1,n−1);
  • Used for identical items.
4. Steps
  1. Enter n,m;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: 4 fruits from 3 types: C(6,4)=15.
6. Common Pitfalls
Unordered;
Top index n+m−1;
Not n^m.

❓ FAQ | Repetition Comb

Formula?
C(n+m−1,m).
Unordered?
Yes.
Vs permutation?
n^m.
Use?
Distribution.
Example?
15.
Bars?
n−1.