Alan, bill, and calvin are playing a game with collectible cards. at the moment, alan has 11 less than 2 1/2 times the number of cards bill has. calvin has 1 more than 1 1/2 times the number of cards bill has. if alan and calvin have the same number of cards, the number of cards bill has is . the number of cards alan and calvin each have is . if alan, bill, and calvin have all the cards in the deck, then the deck has cards.

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 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 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) 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.) (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.)