17. In some dairy states, a kind of base six is used for shipping milk. Six cartons of milk make 1 box; 6 boxes make 1 crate,
6 crates make 1 flat, and 6 flats make 1 pallet. Thus, if someone
said they had filled 2413, that would mean 2 flats, 4 crates,
1 box, and 3 cartons.
a. How many cartons of milk would this be in base ten?

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.)