1. 15 points DevoreStat9 2.E.030. My Notes Ask Your Teacher A friend of mine is

Question

1. 15 points DevoreStat9 2.E.030. My Notes Ask Your Teacher A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 11 of merlot, and 9 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 28 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.) Need Help? Read ItTalk to Tutor

Explanation / Answer

Ans:

a)As serving order is important,so use permutations.

Number of ways=8P3=8!/5!=8*7*6=336

b)Number of ways to select 6 bottles out of 28 bottles=28C6

  =(28*27*26*25*24*23)/(6*5*4*3*2*1)=376740

c)Number of ways to selects 2 bottles of each type=8C2*11C2*9C2=28*55*36=55440

d)Probability to slect 2 bottles of each type=55440/376740=0.147

e)Probability to select all six are of same variety=(8C6+11C6+9C6)/28C6

=(28+462+84)/376740

=574/376740=0.002

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