A friend of mine Is giving a dinner party. His current wine supply Includes 9 bo

Question

A friend of mine Is giving a dinner party. His current wine supply Includes 9 bottles of zinfandel, 11 of merlot, and 8 of cabernet (he only drinks red wine), all from different wineries, If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? 336 If 6 bottles of wine are to be randomly selected from the 28 for serving, how many ways are there to do this? 271262800 If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? 55440 If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? () 0 147 If 6 bottles are randomly selected, what is the probability that all of them are the same variety? ()

Explanation / Answer

a)no of ways serving 3 bottes from 9 bottles = (9C3)*3! = 504

b)no of ways to select 6 bottles from 28 bottles= 28C6 = 376740

c) no of ways to obtain two bottles of each variety = (9C2)(11C2)(8C2) = 55440

d)probality of chosing 2 of each variety when six bottles are chosen =  (9C2)(11C2)(8C2) /28C6 = 0.147

e)no of ways to select 6 bottles such that all bottles are of same variety = (9C6)+(11C6)+(8C6) = 119

Probability to 6 botlles such that all bottles are of same variety = 119//28C6 = 0.00031 ~ 0.001

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