. A friend of ours is giving a dinner party. Her current wine supply includes 8 bottles of zinfandel,
10 of merlot, and 12 of cabernet (she drinks only red wine), all from different wineries.
(a) If she wants to serve 3 bottles of zinfandel and 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?