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, 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 from the 30 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? e) If 6 bottles are randomly selected, what is the probability that all of them are the same variety?

Explanation / Answer

8 - Z
10 - M
12 - C

a)
3 bottles of zinfandel can be selected in 8C3 ways
= 56

b)
6 bottles from 30 can be selected in 30C6 ways = 593775

c)
2 bottles of each variety can be selected in 8C2 * 10C2 * 12C2 = 83160

d)
Probability = 83160/593775 = 0.1401

e)
6 bottles selected are of same variety, this can be done 8C6 + 10C6 + 12C6 = 1162

probability = 1162/593775 = 0.002

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