A friend of mine is giving a dinner party. His current wine supply includes 13 bottles of zinfandel, 11 of merlot, and 7 of cabernet (he only drinks red wine), all from different wineries.
(a) If he wants to serve 3 bottles of zinfandel and serving
order is important, how many ways are there to do this?
ways
(b) If 6 bottles of wine are to be randomly selected from the 31
for serving, how many ways are there to do this?
ways
(c) If 6 bottles are randomly selected, how many ways are there to
obtain two bottles of each variety?
ways
(d) If 6 bottles are randomly selected, what is the probability
that this results in two bottles of each variety being chosen?
(Round your answer to three decimal places.)
(e) If 6 bottles are randomly selected, what is the probability
that all of them are the same variety? (Round your answer to three
decimal places.)
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