A friend of mine is giving a dinner party. His current winesupply includes 12 bottles of zinfandel, 8 of merlot, and 10 ofcabernet (he only drinks red wine), all from differentwineries.
(a) If he wants to serve 3 bottles of zinfandel and servingorder is important, how many ways are there to do this?
ways
(b) If 6 bottles of wine are to be randomly selected from the 30for serving, how many ways are there to do this?
ways
(c) If 6 bottles are randomly selected, how many ways are there toobtain two bottles of each variety?
ways
(d) If 6 bottles are randomly selected, what is the probabilitythat this results in two bottles of each variety being chosen?(Round your answer to three decimal places.)
(e) If 6 bottles are randomly selected, what is the probabilitythat all of them are the same variety? (Round your answer to threedecimal places.)
