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Question: a friend of mine is giving a dinner party his...

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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, all from different wineries. He will serve five bottles of the wines during dinner in a particular order.

(a) How many distinct sequences are there of serving any five wines?

(b) If the first two wines have to be zinfandel and the last three must either be merlot or cabernet, how many ways can this be done?

(c) If the wine sequence is formed randomly, what is the probability that none of the wines served is a zinfandel?

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