Experiments with random selection: when to respect order? I have a hard time imagining experiments of this nature without noting the arrangements (I draw that ball with my left hand, the other with my right. I draw that ball first, the other second) so I'm naturally inclined to imagine sample spaces that respect order. However, I don't think this is always the right convention to adopt so I'm looking to see if it can be generalized as to when to respect order and when to disregard it.
As an eample: An urn contains five red, three orange, and two blue balls. Two balls are randomly selected.  What is the sample space of this experiment? My thoughts are that we either pay attention to arrangement and the sample space is $$S={BB, BO, BR, OB, OO, OR, RB, RO, RR}$$ or we simply care about the combinations and the sample space is $$S={BB,BO, BR, OO, RO, RR}.$$
Is there anything in the statement of the question that indicates which sample space to use? 
 A: The example problem is sloppily worded because it doesn't specify what it means by "randomly selected".
It turns out, however, that the following three descriptions give rise to the same distribution:


*

*Select one ball uniformly from the urn, then select another ball uniformly among those left in the urn, then forget which order you selected the two balls in.

*Select an ordered pair of balls uniformly among all ordered pairs that don't have the same first and second element, then forget the order of the pair.

*Select an unordered pair of balls uniformly among all unordered pairs of balls.
Your point, if I understand you correctly, is that it is difficult to imagine a physical procedure that realizes (3) directly. (I'm not so sure about that -- for example you could start by enumerating all of the unordered pairs, write each of them on a piece of paper, and then draw one of the papers uniformly. But never mind that).
In any case, you probably agree that at least (1) is "physically" meaningful. And in applications where the order actually doesn't matter, saying (3) instead of (1) is convenient because it abstracts away details that may not be relevant in the rest of the reasoning.
It's the simplest way to describe the resulting distribution, even though we may (or may not) need to switch to (1) either for carrying out the experiment or for analyzing whathever it is we're doing with the chosen balls.
Note that in all of the three cases we need to distinguish between different balls of the same color until we're done choosing and have our distribution. For example, for neither of your two sample spaces can you assume that every outcome is equally likely.
