A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 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? b. ?If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this? c. ?If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? d. ?If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? e. ?If 6 bottles are randomly selected, what is the probability that all of them are the same variety?
Answer : Step 1 of 5 : A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet (he only drinks red wine), all from different wineries. a) The number of zinfandel bottles be n =8 The number of zinfandel bottles served be r = 3 If he wants to serve 3 bottles of zinfandel and serving order is important, then the number of ways for selecting 3 out of 8 is 8P3 n! Formula for permutation is P(n, r) = (n r)! where , n = 8 and r = 3 8! P(8, 3) = (8 3)! = 40320 120 = 336 336 ways are there to do.
