Evan's nightly chores include washing dishes. His mother cooks everything she prepares a bit too long. Because of this, Evan spends a lot of sweat, effort, and time washing dishes. He sees a commercial on television that claims a new dishwashing detergent, called Brand X, cuts through grease better than its competitor, called Brand Y. They back up their claim with testimonials from people who say they've used this new detergent. What is a possible testable question (in correct format) that Evan might ask for this scenario? Which detergent will remove grease better brand X or brand Y.

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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.)