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2001 AMC 10 Problem 19

Problem 19 of 25HarderCounting & Probability

Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible?

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Solution

The number of selections is the number of nonnegative integer solutions of g+c+p=4.g+c+p=4. By stars and bars, this is (4+22)=(62)=15.\dbinom{4+2}{2}=\dbinom62=15. Thus, the correct answer is D.

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Concepts: stars and bars · combinations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.