I suppose upon further review it's open to interpretation, but "a true function from scientists to fields" to me means that each scientist must map to exactly one field; that is, you can't have two different answers for scientist 2 - you would have f(2) = B and f(2) = D at the same time. And, you can't have no answer for scientist 5 (that is, f(5) = undefined).
I conceptualized the problem as a Scantron test - there are 5 questions (the 5 scientists) and for each, you can pick one of the 5 fields. As I said, it's possible this is not what the OP intended, but that's how I read it.
Heh, also, strictly as a matter of choice and personal preference, if I were doing this in real life, I would probably find which of the eight choices that could actually be correct is the most likely, and pick that one - I don't think the perfectionist in me would allow me to put down a set of answers that isn't consistent with itself (or with what I remember for sure).
Given that restriction, I think the best you can do is BDCAE or BDACE, both of which have an expected score of 19/8 = 2.375.