Probability Question!

Hi.
I'm having a lot of trouble with these types of problems. I'd really appreciate it if you could show me how to solve this one correctly. Thanks.

Question:
A town council consists of 8 Democrats, 7 Republicans, and 5 Independents. A committee of 3 is chosen by randomly pulling names from a hat. What is the probability that the committee has:
a) 2 Dems and 1 Rep?
b) 3 Independents?
c) no Independents?
d) 1 Dem, 1 Rep, 1 Independent?

Thanks again

d) \(\displaystyle \frac {\binom {8}{1} \binom {7}{1} \binom {5}{1}} {\binom {20}{3}}\)
All are done is a similar way.