riend mine is giving a dinner party. His current wine supply includes / bottles of zinfandel, 11 of merlot, and 13 of cabernet (he only drinks red wine), all from diferent 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.)

MATLAB: An Introduction with Applications
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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 (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?
(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.)
Transcribed Image Text: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 (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? (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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Comments: As per our guidelines we are supposed to answer only three subparts. Kindly repost other parts in the next question.

Solution:

Given information:

The number of zinfandel bottles = 7

The number of merlot bottles = 11

The number of cabernet  bottles = 13

Total bottles = 7+11+13 = 31

 

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