A friend of mine is giving a dinner party. His current wineries. wine supply ind
ID: 3306724 • Letter: A
Question
A friend of mine is giving a dinner party. His current wineries. wine supply indludes s bottles of zinfandel, 9 of merlot, and 10 of cabernet (he only drinks red wine), all from differ a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? 990 ways If o bottles of wine are to be randomly selected from the 27 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 If 6 bottles are randomly selected, what is the probability that all of therm are the same variety? (Round your answer to three decimal places)Explanation / Answer
a)
There are 8 bottles of zinfandel,
Number of ways three bottles are chosen where order is importent is 8P3
8P3 = 8! / (8-3)! = 336
b)
6 bottles of wine are randomly selected from 27 bottles by 27C6 ways.
27C6 = 27! / [ (27-6)! * 6! ] = 296010
c)
Number of ways that 2 bottles of each variety can be chosen from randomly selected 6 bottles is
8C2 * 9C2 * 10C2 = 45360
d)
P(2 bottles of each variety chosen from 6 bottles)
=n(2 bottles of each variety chosen from 6 bottles) / n( 6 bottles are chosen from 27 bottles)
= 45360 / 27C6
= 45360 / 296010
=0.153
e)
p(All bottles are same veriety from 6 bottles)
= n(All bottles are same veriety from 6 bottles) / n( 6 bottles are chosen from 27 bottles)
= ( 8P6 + 9P6 + 10P6 ) / 27P6
= 231840 / 213127200
= 0.001