My Notes 11 -5 points DevoreStat9 2.E.030 A friend of mine is giving a dinner pa

Question

My Notes 11 -5 points DevoreStat9 2.E.030 A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 12 of merlot, and 10 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 ae to be randomly selected from the 31 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

9 bottles of Z, 12 of M and 10 of C

a)
3 bottles from 9 bottles of zinfandel in 9C3 ways
= 84

b)
6 bottles from 31 bottles can be selected in 31C6 ways = 736281

c)
2 bottles of Z can be selected in 9C2 ways
2 bottles of M can be selected in 12C2 ways
2 bottles of C can be selected in 10C2 ways

Required number of combinations are 9C2*12C2*10C2 = 106920

d)
Required probability = 106920/736281 = 0.1452

e)
6 bottles of Z can be selected in 9C6
6 bottles of M can be selected in 12C6 ways
6 bottles of C can be selected in 10C6 ways

Required probability = (9C6 + 12C6 + 10C6)/31C6 = 1218/736281 = 0.00165

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