I came across the article
Subjective Probability: A Judgment of Representativeness Daniel Kahneman and Amos Tversky
and in particular their following example
I have a lot of difficulties in understanding the question
In many rounds of the game, will there be more results of type I or of type II?
My difficulties are the following. IMHO the question leads to misunderstandings. There are two possible scenarios that I'm considering.
1 case: Does the order of the numbers play a role?
If so, than, it should be equally likely to get the event $$44543 \qquad \text{or} \qquad 44444$$
2 case: Does the order of the numbers not play a role?
If so, than it is way more likely, to get the event containing three $4$, one $5$ and one $3$, than to get all five $4$s. This is because the number of strings of length $5$ containing three $4$, one $5$ and one $3$ is $$\frac{5!}{3!} = 5\cdot 4 = 20.$$
The problem is that I don't see any other scenario, but the author says
The uniform distribution of marbles II (so the event that we get five $4$s) is, objectively, more probable than the nonuniform distribution I.
I looked out what it meant for him the word "objectively" and it is intended to be as precise as a mathematical explanation should be.
You're right in most of what you write. It's quite misleading, especially with the word “type”, which seems to suggest that all results with the same number of $3$s, $4$s and $5$s are subsumed. As you say, the uniform distribution is much less probable than all results of “type” I together.
However, it's not true that the uniform distribution and a specific instance of “type” I are equally likely. The uniform distribution has $\binom84=70$ ways to select marbles for Carl and Ed, and the other one only has $\binom85=56$. (This touches on another very sloppy aspect of the text: It says “at random” and doesn't specify a distribution. However, I think we can assume that they intended to imply “independently uniformly”.)
Too bad – someone gave me a book by Kahnemann and Tversky for my birthday; I was hoping to find the time to read it – that doesn't sound like such a promising prospect anymore now...