1. +-15 points DevoreStatg2. E.030 My Notes Ask Your Teacher A friend of mine is
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1. +-15 points DevoreStatg2. E.030 My Notes Ask Your Teacher A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 10 of merlot, and 8 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 27 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.)Explanation / Answer
a) number of ways 3 bottles of zinfandel can be served = 9*8*7
The order can be interchanged.
So, 9*8*7*3= 1512
b)Ways 6 bottles can be randomly selected = 27*26*25*24*23*22
c) obtain 2 of each
2 zinfandel = 9*8
2 merlot= 10*9
2 cabernet 8*7
9*8*10*9*8*7
d) probability = favourable/ total
and from (c) / 27!
(as 27! are total number of ways bottle can be randomly selected)
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