1. -5 points DevoreStat9 2.E.030 Notes Ask Your Teacher A friend of mine is givi

Question

1. -5 points DevoreStat9 2.E.030 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 11 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 30 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 to serve 3 bottles of zinfadel = 9P3 = 9! / (9-3)! = 504

b) Number of ways to slect 6 bottles of wine = 30C6 = 30! / (6! * (30-6)!) = 593775

c) Number of ways to obtain two bottles of each variety = 9C2 * 10C2 * 11C2 = 36 * 45 * 55 = 89100

d) P(two bottles of each variety is choosen) = 89100 / 593775 = 0.15

e) P(all of them are of same variety) = P(all are zinfadel) + P(merlot) + P(cabernet)

                                                           = (9C6 / 30C6) + (10C6 / 30C6) + (11C6 / 30C6)

                                                           = (84/593775) + (210/593775) + (462/593775)

                                                           = 0.001

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