Ensemble Averages and Binomial Expansion

Hello. I'm having trouble with one question on the first assignment of a statistical physics course, mostly because I don't understand what the question is asking overly well. If somebody could help clarify what this question is asking me to find that would be wonderful. (I'm a bit iffy on some of the notation because my textbook has yet to arrive in the mail, which is part of the problem).

Anyways, I've attached the question as an image here.

http://img816.imageshack.us/img816/2...1question3.jpg

Thank you very much for your help.