A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of Zinfandel, 10 of Merlot, and 12 of Cabernet (he only drinks red wine), all from different wineries.

a) If he wants to serve 3 bottles of Zinfandel and the serving order is important, how many ways are there to do this?

b) If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this?

c) If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety?

d) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen?

e) If 6 bottles are randomly selected, what is the probability that all of them are the same variety?