2001 AMC 10 Problem 19

Question

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

Small hint:

Count nonnegative integer solutions of

g+c+p=4

Big hint:

Use stars and bars:

\dbinom{4+2}{2}

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.