Max Stamp approves study abroad documents for the university. Students must wait in line with their forms outside Max's office. One student at a time is allowed in his office and Max takes precisely 15 minutes to evaluate each student’s set of documents. On average, 2 students per hour go to his office and they spend, on average, 160 minutes trying to get their forms approved (time waiting in queue plus time in Max’s office having him evaluate their documents). On average, how many students are waiting outside of Max’s office?

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.)