[Nate]

I was talking about this post, in which Max gives the list of possible final scores for five balls:

It's entirely true.

I just looked up the term "sample space" (admittedly only on Wikipedia), and all it is, is the set of all possible outcomes. In the case of your homework, the sample space is:

{5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35}