The amount of caffeine consumed from a glass of diet pepsi is proportional to the number of ounces that was drank. the table below shows the amount of caffeine consumed by three different people and the corresponding number of ounces of diet pepsi that they each drank. amount of caffeine (mg) 24 36 48 amount of diet pepsi (oz) 8 12 16 what is the unit rate (or constant of proportionality)? write an equation to represent this proportional relationship. make sure to define the variables you used.

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.)