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A friend is hosting a party. Her wine cellar has 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet, all from di§erent wineries.
(a) If she wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to serve?
(b) If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to serve?
(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?
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