A friend of mine is giving a dinner party. His current wine supply includes 7 bottles of zinfandel, 9 of merlot, and 13 of cabernet (he only drinks red wine), all from different wineries. (a) If he...

Extracted text: A friend of mine is giving a dinner party. His current wine supply includes 7 bottles of zinfandel, 9 of merlot, and 13 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? 210 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? 475020 ways (c) If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? 58968 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. .124 (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.) 3.804