A friend of mine is giving the dinner party. His current wine supply comprises 8 bottles of zinfandel, 11 of merlot, and 9 of cabernet (he only drinks red wine), all from different wineries.
(a) If he desires to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this?
(b) If six bottles of wine are to be randomly chosen from the 28 for serving, how many ways are there to do this?
(c) If 6 bottles are randomly chosen, how many manners are there to obtain two bottles of each variety?