A friend of mine is giving a dinner party. His current wine supply includes 8 bo

Question

A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 12 of merlot, and 9 of cabernet (he only drinks red wine), all from different wineries. If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? i If 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? 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.) 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.)

Explanation / Answer

a)

As order is important, we use permutations,

8P3 = 8!/(8-3)! = 336 [ANSWER]

b)

It seems the order is not important here, so we use combinations,

29C6 = 29!/(6!23!) = 475020 ways [ANSWER]

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c)

There are

#ways = (8C2)*(12C2)*(9C2) = 66528 ways [ANSWER]

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d)

From B and C,

P = 66528/475020 = 0.14005305 [ANSWER]

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e)

There are

#ways = 8C6 + 12C6 + 9C6 = 1036 ways to do it.

Hence,

P = 1036/475020 = 0.002180961 [ANSWER]

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