l- #30 (book) 30. A friend of mine is giving a dinner party. His current wine su
ID: 3040913 • Letter: L
Question
l- #30 (book) 30. 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 (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? If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this? b. c. 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 proba- bility that this results in two bottles of each varicty being chosen? If 6 bottles are randomly selected, what is the proba bility that all of them are the same variety? d. e.Explanation / Answer
a) no of ways = 8p3 = 336
b) no of ways = 30C6 = 593775
c) no of ways = 8C2 * 12C2 * 10C2 = 83160
d) probability = 8C2 * 12C2 * 10C2/30C6 =0.14
e) probability = 8C6/30C6 + 12C6/30C6 + 10C6/30C6 = 0.002
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