Rich Harang

Here are the solutions to the extra problems. 

If you did the combinatorics problems differently, check the numerical answers to see if mine matches yours.  There's usually several valid ways to think of any of them.  If you are off by a factor of 2 on 7b and 8c, and/or a factor of 6 on 8a, note it for future reference but don't worry too much about it; nothing that complex will be on the midterm or final.