Why are we excluding red, green, red?
The contents of the urn would still be a set, but if the contents were initially drawn from a binomial distribution, calling out the possible combinations is required for purposes of counting, ie figuring the probability of each combination.
People intuitively know that there are more ways to have two green and one red than three reds. That maps to most things in the real world too. This question sort of tricks people.
> n of them are red, and 100-n are green, where n is chosen uniformly at random in [0, 100].
N is chosen first, and that many red balls are put in. You don't flip a coin 100 times and then determine N from how many heads you flipped, that would be a tortuous interpretation from my pov, and would violate the requirement that N is chosen uniformly, so it seems like it's right there in the question.
The way you can know this is: ask people the same question with "binomial" instead of "uniform" and see if you get a different answer. My guess is people will say the same regardless.
> n is chosen uniformly at random
If the balls follow a binomial distribution, then your intuition would say that N wasn't the thing that was chosen; the balls were chosen, and then N was determined afterwards by counting the balls that you picked. This is because you cannot choose N and then draw balls binomially and get that many green or red balls. You'd have to choose 100 balls, see whether the number of Red matches your chosen N, and if it didn't, draw again, which is a tortuous interpretation given the phrasing, as I said above.
By saying that N was "chosen", it implies to me that N comes first, and the choice of balls comes after that, i.e. the balls are not binomially distributed.
Wouldn't you need some extra parameters if it were a binomial distribution though? For a uniform distribution every item is equiprobable (i.e. there's only one uniform distribution for a given N) but there are many binomial distributions possible for a given N. (Disclaimer, I know very little about statistics.) So the fact that you aren't given those parameters in the question means you can't make much of a prediction if it were binomial.
Edit: I read that binomial distributions are parameterized on both the number of trials and the probability of the two outcomes, so that kind of demonstrates my point doesn't it? You're not given the probability of Red and Green for the binomial distribution, so you can't really answer the question that way. You could assume it's 50/50, but that's an assumption that isn't justified by the question.