Combinations with Repetition Calculator
Combinations with Repetition Calculator
Enter how many types are available (n) and how many you're choosing (r), and this calculator finds the number of combinations when the same type can be picked more than once.
Unlike ordinary combinations, where each item can only be chosen once, this allows the same type to be picked multiple times — like scooping 3 ice cream flavors from 5 available options, where nothing stops you from picking the same flavor twice or even three times. The formula turns out to be an ordinary combination in disguise once you know the trick: C(n+r−1, r), a clever transformation that converts the "with repetition" counting problem into a standard combination calculation, which is a genuinely elegant piece of combinatorics once you see how the substitution works.
- Combinations with repetition allow the same item to be chosen multiple times, unlike ordinary combinations where each item can only be picked once — like scooping 3 ice cream flavors from 5 available, where you could pick the same flavor twice.
- The formula reduces to an ordinary combination in disguise: C(n+r−1, r), which accounts for the extra ways repeated choices can be arranged.
- This is also known as a "multiset coefficient," since it counts multisets (collections that allow duplicates) of size r drawn from n types.
How do combinations with repetition differ from ordinary combinations?
Ordinary combinations only let you pick each item once, while combinations with repetition let you pick the same item multiple times, using the formula C(n+r−1, r) instead of C(n, r).
How many ways can you choose 3 flavors from 5, allowing repeats?
C(5+3−1, 3) = C(7,3) = 35.
Combinations with Repetition Calculator
Enter how many types are available (n) and how many you're choosing (r), and this calculator finds the number of combinations when the same type can be picked more than once.
Unlike ordinary combinations, where each item can only be chosen once, this allows the same type to be picked multiple times — like scooping 3 ice cream flavors from 5 available options, where nothing stops you from picking the same flavor twice or even three times. The formula turns out to be an ordinary combination in disguise once you know the trick: C(n+r−1, r), a clever transformation that converts the "with repetition" counting problem into a standard combination calculation, which is a genuinely elegant piece of combinatorics once you see how the substitution works.
- Combinations with repetition allow the same item to be chosen multiple times, unlike ordinary combinations where each item can only be picked once — like scooping 3 ice cream flavors from 5 available, where you could pick the same flavor twice.
- The formula reduces to an ordinary combination in disguise: C(n+r−1, r), which accounts for the extra ways repeated choices can be arranged.
- This is also known as a "multiset coefficient," since it counts multisets (collections that allow duplicates) of size r drawn from n types.
How do combinations with repetition differ from ordinary combinations?
Ordinary combinations only let you pick each item once, while combinations with repetition let you pick the same item multiple times, using the formula C(n+r−1, r) instead of C(n, r).
How many ways can you choose 3 flavors from 5, allowing repeats?
C(5+3−1, 3) = C(7,3) = 35.