Probability ice cream flavor problem

[nahanksh]

Homework Statement

There are four ice cream flavors; chocolate,cookies,strawberry and vanilla.

How many different combination of flavors of three scoops of ice cream are possible if it is permissible to make all three scoops the same flavor?

Homework Equations

The Attempt at a Solution

The answer is 20.

But i am very confused about the wording of the question.
If only all three scoops with same flavor is counted as a different combination, shouldn't it be just 4(three scoops of same four flavors) + 4*3*2 ( all different flavors combination)

then it gives me 28 which is wrong..

What's the point of this question and how to approach to it?

Could someone help me out here?

 

[Audaciity]

4*4*4 = 64 possibilities

 

[vela]

The 4*3*2 you calculated is the number of permutations, but the question asks for the number of combinations.

The question is a bit unclear, but I think I understand what they want. The possibilities you have for constructing flavor combinations are: 3 scoops all different flavors, 3 scoops all the same flavor, and 2 scoops of one flavor and 1 scoop of a second flavor. They seem to be counting, for example, two scoops of strawberry and one scoop of vanilla as a different flavor combination from two scoops of vanilla and one scoop of strawberry. If you add all those up, it comes out to 20.