Combinations with Repetition
Count selections of r items from n, with repetition allowed.
Choosing with repeats allowed
When you can pick the same item more than once and order does not matter — like scoops of ice cream from a set of flavors — ordinary combinations undercount. This tool uses the multiset formula.
Choosing 3 scoops from 5 flavors, with repeats allowed, gives 35 combinations. The formula is n plus r minus one, choose r, and it grows quickly with either number.
Exact and private
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Frequently Asked Questions
What is this?
The number of ways to choose r items from n types when repeats are allowed and order does not matter — the multiset coefficient.
What is the formula?
It equals n plus r minus one, choose r.
Where is it used?
Counting combinations like scoops of ice cream from flavors, or distributing identical items into groups.
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