Combinations with Repetition Calculator

About this calculator

This calculator counts combinations with repetition (also called multiset coefficients) — the number of ways to choose r items from n types when repeats are allowed and order doesn't matter — using the formula C(n+r−1, r) = (n+r−1)! / (r!·(n−1)!). The formula comes from the “stars and bars” technique: representing each selection as a row of r stars split into n groups by n−1 bars, which turns the counting problem into an ordinary combination C(n+r−1, r).

Students and instructors in combinatorics and discrete math courses use it to work through classic examples like choosing r scoops from n ice cream flavors with repeats allowed, or distributing identical objects into distinguishable bins; computer scientists use the same math to count multisets and evaluate generating functions; and statisticians use it when analyzing sampling schemes done with replacement. Enter the number of types (n) and the number chosen (r) to get the count.