2001 AMC 10 Problem 19

Attempt Problem 19 of the 2001 AMC 10 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 10 solutions, or check the answer key.

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19.

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?

$6$

$9$

$12$

$15$

$18$

Answer: D

Concepts:stars and bars combinations

Difficulty rating: 1340

Solution:

The number of selections is the number of nonnegative integer solutions of $g+c+p=4.$ By stars and bars, this is $\dbinom{4+2}{2}=\dbinom62=15.$

Thus, the correct answer is D.

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