If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then torricelli's law gives the volume v of water remaining in the tank after t minutes as v=5000(1−t40)20≤t≤40. find the rate at which water is draining from the tank after the following amount of time. (remember that the rate must be negative because the amount of water in the tank is decreasing.)

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.)