Use a generating function (and computer algebra system) to determine the number of ways she can distribute the cookies so that each volunteer receives at least two cookies and no more than seven cookies.
I don't know how to do generating functions. Can someone explain the concept and help me apply it to this situation?
$(x^2 + x^3 + x^4 + x^5 + x^6 + x^7)^6$
The coefficient of $x^{30}$ is 3431.