Identifying a Permutation problem vs a Combination problem I understand that combination is used when the order of something doesn't matter. For the most part I can differentiate between the two. But there are times when I am almost certain something is combination based and it ends up being permutation. This problem for example : 
In the Sociology Department there are 8 female faculty members and 9 male faculty members. 
Either 2 female faculty members or 2 male faculty members will be chosen and assigned the following tasks:
play on the departmental co-ed rugby team; team-teach a liberal arts course.
How many different outcomes are possible, assuming that nobody will be assigned more than one task?
My solution was $\binom82$+$\binom92$. The actual solution was the same but with a permutation. I am curious as to how the order matters here. In my mind i'm thinking it does not matter which female or male faculty matters are chosen either way 2 of each faculty will be chosen. Is this the wrong way to assess the problem? Can someone give me a thorough explanation on some key words to look out for to differentiate between the two so that I do not make such careless errors on my exam.
Thank you!
 A: The key is that one of them will play rugby and one will teach liberal arts. The way this connects to "the order matters" is you can imagine that the first faculty member selected will play rugby and the second selected will teach liberal arts. 
This is contrast to something where they are, say, selected to be on a committee. Then the committee having teacher $A$ and teacher $B$ on it is the same outcome as the committee having having teacher $B$ and teacher $A$ on it. In this situation you would use combinations.
Note that this is really different from your question. The outcome where teacher $A$ plays rugby and teacher $B$ teaches liberal arts is different from the outcome where teacher $B$ plays rugby and teacher $A$ teaches liberal arts.
A: The part that is most important is:

...play on the departmental co-ed rugby team; team-teach a liberal arts course.

Because it tells you that there are 2 choices. You can make it more clear by pretending the male and female faculty members line up in separate lines randomly and the first 2 in the line are chosen. The first goes to the departmental co-ed rugby team and then the second the liberal arts course. Then switch the order of the first 2 and see if it makes a difference to who goes where.
