The city housing authority has received 75 applications from qualified applicants for ten low-income apartments. five of the apartments are on the north side of town, and five are on the south side. if the apartments are to be assigned by means of a lottery, find the following probabilities. (a) a specific qualified applicant will be selected for one of these apartments. (round your answer to three decimal places.) (b) two specific qualified applicants will be selected for apartments on the same side of town. (round your answer to five decimal places.)

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.)