A friend of mine is giving a dinner party His current wine s

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. If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways If 6 bottles of wine are to be randomly selected from the 28 for serving, how many ways are there to do this? ways If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways 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.) 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.)

Solution

a) here bottle for zinfadel = 8

we need 3

= 8C3 = 56

B) 6 BOTTLES TO BE SELECTED = 28C6 = 376740

C)2 OF EACH TYPE = 8C2*11C2*9C2 = 55440

D)TOTAL WYS TO SELECT TWO OF EACH TYPE = 55440

HENCE THE PROBAILITY = 6/55440=0.0001

E)SAME VARIETY GETTING WAYS = 11C6 = 462

PROBABILITY = 6/462= 0.012