A friend of mine is giving a dinner party. His current wine supply includes 7 bottles of zinfandel, 11 of merlot, and 13 of cabernet, 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?

(b) If 6 bottles of wine are to be randomly selected from the 31 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? (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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