Please help !!! My Notes A friend of mine is giving a dinner party. His current
ID: 3069182 • Letter: P
Question
Please help !!! My Notes A friend of mine is giving a dinner party. His current wine supply includes 10 botties of zinfandel, 8 of meriot, and 9 of cabernet (he only drinks red wine) (a) It he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? all from different wineries ways (b) If 6 bottles of wine are to be randomly selected from the 27 for serving, how many ways are there to do this? 18 x ways (c) ir 6 bottles are randomly selected, how many ways are there to obtain two botties of each variety ways (d) If 6 botties are randomly selected, what is the probability that this resuits in two bottles of each variety being chosen? (Round your answer to three deomal places) (e) ir 6 bottles are randomly selected, what is the probability that all of them are the same variety? (Round your answer to three decimal placesExplanation / Answer
10: Zin
8: Mer
9: Cab
(a):
He wants to serve 3 bottles of Zin and the order is important, then it is an arrangement and not a selection
So, required ways = P(10, 3) = 10*9*8 = 720
Had the order not been that important, then the number of ways would have been C(10, 3) = 120
(b):
Select 6 out of 27
No. of ways = C(27,6) = 296,010
(c):
Of the 6, we need 2 from each variety
Required ways= C(10,2) * C(9,2) * C(8,2)
= 45*36*28
= 45,360
(d):
Required Probability = C(10,2) * C(9,2) * C(8,2)/ C(27,6)
= 45360/296010
= 0.153
(e):
All of them are same variety = (C(10,6) + C(9,6) + C(8,6))/C(27,6)
= 322/296010
= 0.00108
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