A friend of mine is giving a dinner party. His current wine supply includes 9 bo
ID: 3055422 • Letter: A
Question
A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 11 of merlot, and 12 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 32 for serving, how many ways are there to do this? ways (c) Ifo bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d If ? bottles are randomly selected, what is the probability that this results in two bottles of each var ety 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
a)
a) number of ways to select 3 out of 9 =9P3 =404
b)number of ways =32C6 =906192
c) numbr of ways =9C2 *11C2 *12C2 =130680
d)probability =130680/906192 =0.144
e) probability that all are same =(1/906192)*(9C6 +11C6 +12C6 ) =0.002