The question usually doesn't matter, what I do notice that I is that I'm almost always wrong. But I can give an example of a question:
Q Three Americans, three Canadians, three Spaniards, and three Russians are flying on a small plane that consists of 6 rows of two seats each. In how many ways can they be seated, so that no two people from the same country sit in the same row?
A We first count the number of seatings where two Americans sit in the same row. There are six rows to choose from. Once the row is chosen, there are 2 $\cdot$ 3 = 6 ways to seat the Americans in a row.
How I would answer it, and immediately get it wrong from the get-go, is that I would ask myself in how many ways I can choose two people from a certain nationality out of three persons from that nationality.
I would think that order doesn't matter. If I chose person1 and then person2, how does that differ from choosing person2 first and then person1? In other words, I would go for 3C2.
Then you could argue that the seats matter; that, in a given row, it matters where person1 sits and where person2 sit, and hence it is 3 $\cdot$ 2 and not 3C2. But I don't see how I would get that information from the question as it is.
This same problem for me applies to the rows as well; from the answer it is implied that not only the seat but also the row where a person sits, matters. Again, how does this flow from the question?
Q2 Yeechi has a deck of cards consisting of the 2 through 5 of hearts and the 2 through 5 of spades. She deals two cards (at random) to each four players. What is the probability that no player receives a pair?
A2 First we count the number of ways the first player receives a pair. There are four possible pairs (one for each denomination from 2 through 5), and the number of ways the remaining six cards can be dealt to the remaining three players is 6C2 $\cdot$ 4C2 = 90, because we have 6C2 choices for cards for the first remaining player, then 4C2 choices for cards for the next remaining player.
Next we count the number of ways both the first player and second player can receive a pair. There are four possible pairs for the first player, and three possible pairs for the second player. (sic)
Once again, I did not choose for 4 $\cdot$ 3, but for 4C2. For me, there's nothing that indicates that the order matters here. What does it matter that player 1 has pair 1 and player 2 has pair 2, or that player 1 has pair 2 and player 2 has pair 1, as long as they have a pair!
I really could use some help in getting my thinking straight about these matters, because this keeps tripping me up continuously.
I agree that the first question could be perceived to be a bit vague.
Although not infallible, some keywords often help to distinguish between permutations and combinations.
Permutations: Arrange, order, ways.
Combinations: Select, choose.
From a practical point of view, though, the row and particular seat (e.g. window or aisle) do matter, and that is how I would interpret it. What you could do if you have a strong doubt is to spell out the doubts you are having and the assumptions you are making, or better still, offer two sets of answers.
For the second question, it doesn't matter, probability is being asked for, and if you compute favorable and total outcomes in a consistent manner, the ratio will not change !