Paulo wants to buy an ice cream with four scoops at an ice cream shop that offers three flavors: açaí, vanilla, and cajá. In how many different ways can he make this purchase?
(a) 6
(b) 9
(c) 12
(d) 15
(e) 18
The correct option is (d).

Let's denote each flavor of ice cream by its initial letter, that is, a - açaí, $b$ - vanilla, $c$ - cajá. To enumerate all the possibilities of buying an ice cream with four scoops, we must consider the following cases:

- four scoops of the same flavor (1st column on the side);
- three scoops of the same flavor and one of a different flavor (2nd column on the side);
- two scoops of one flavor and two of another flavor (3rd column on the side);
- two scoops of one flavor and the other two of the other two flavors (4th column on the side).

| $a a a a$ | $a a a b$ | $a a b b$ | $a a b c$ |
| :---: | :---: | :---: | :---: |
| $b b b b$ | $a a a c$ | $a a c c$ | $b b a c$ |
| $c c c c$ |  | $b b c c$ | $c c a b$ |
|  | $b b b a$ |  |  |
|  | $b b b c$ |  |  |
|  |  |  |  |
|  | $c c c a$ |  |  |
|  | $c c c b$ |  |  |

Thus, we obtain 15 ways to make this ice cream purchase.