Sheila has an exam tomorrow, but wants to go out with her friends. Her roommate tells her that she probably should plan on getting back before midnight, but the roommate does not give any reasons to support her statement. Should Sheila regard the roommate's advice as trustworthy?
(a) Yes, the roommate has Sheila's best interests in mind.(b) No, the roommate is not a good student herself.(c) Yes, the roommate went to the same high school as Sheila.(d) No, the roommate is not experienced enough to be trustworthy.

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.)