I am trying to study for my finals and I am stuck. We were given a practice exam that we are allowed to use as notes for the final, but there are two questions that I am struggling with. I have posted them below. I'm hoping that someone can walk me through the steps to find a solution.

1. Set up a generating function and use it to find the number of ways in which eleven identical coins can be put in three distinct envelopes if each envelope has at least two coins in it.

2. Set up a generating function and use it to find the number of ways in which eleven identical coins can be put in three distinct envelopes if each envelope has most six coins in it.