My problem is: Assume that every time you buy a box of cereal, you receive one of the pictures of the New York Yankees players and there are $n$ on the team. Over some time you buy $m\ge$$n$ boxes of cereal. Use the Inclusion-Exclusion principle to show that the probability that you will get all $n$ pictures is: $1- {n \choose 1}({n-1 \over n})^m + {n \choose 2}({n-2 \over n})^m \ldots + (-1)^{n-1}{n \choose n-1}({1 \over n})^m $
I am new to this principle and to combinatorics in general so I may be missing some key information or obvious details. I understand that we have a point of reference so that the first term will always be $1$ but I do not understand how we can generate the other terms or where they come from in context of the problem.