Some comments from Jose

1. I did not grade problem #1, but looking over it I found that a lot of people got 6!. This makes no sense since there are only 4 variables! Please review the multinomial theorem.
2. The answer in problem #3 should be simplified.
3. I would recommend that you learn a method for counting "composition like problems" and use it instead of memorizing formulas. A saw a lot of attempts to use the formulas of Chapter 5, where n and k were interchanged and as a result you got a wrong answer. I usually know how to count compositions using the method of "bars and stars" (if you want -- come to my office hours and I'll show you how I remember) and deduce everything else from that one.
4. If you are going to use the composition formula you should explain why you can use it in your particular problem. This especially applies to Problem #5 (the one with the billiards balls) in this homework.
5. Finally, you should ALWAYS justify your answers and show how you got them. Just an answer is not worth full credit. Furthermore, if you have a wrong answer but you have good ideas, I may give you some partial credit.