ut it is alieauy owhed? 30. A friend of mine is giving a dinner party. His curre
ID: 3355612 • Letter: U
Question
ut it is alieauy owhed? 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? b. If 6 bottles of wine are to be randomly selected fror the 30 for serving, how many ways are there to du 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 proba- bility that this results in two bottles of each variety being chosen? e. If 6 bottles are randomly selected, what is the proba- bility that all of them are the same variety?Explanation / Answer
a) No. of ways = 8 * 7* 6 ( Since order is important) = 336
b) No. of ways = 30C6 = 30*29*28*27*26*25 / 720 = 593775
c) No.of ways = 8C2 * 10C2 * 12C2 = 28* 45* 66 = 83160
d)Probability = 83160/593775= 0.1400
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