Recently, I answered a question on Math.stackexchange, but it turned out to be wrong. However, I do not know why it is wrong. Is it appropriate to create new questions asking about why the answer I wrote was wrong for the question?
(a) Yes it is totally appropriate to ask a new question inquiring about the old question. Describe the setting from scratch in the new question so the other users don't have to follow a link in order to understand what you're asking, but also definitely do provide a link to the old question you are asking about.
(b) But maybe in this case I can save you a step? Based on your posting history I assume you are thinking of this question:
IMO, your answer is correct for the question as it is written. Your answer differs from the accepted answer because both the OP, and the accepted answer, are implicitly assuming (without stating it) that the group selected for the carpool has a fixed prespecified size $k$, while your answer is addressed to counting carpools of all sizes from $1$ to $n$.