To determine whether dogs prefer a specific brand of dog food to that of a competitor, market researchers are working with a local dog shelter to randomly select dogs for participation in a study. All randomly selected dogs are put into a large room with two bowls of food — one with their brand and another with the competitor's brand. The first two dogs immediately go for the dog food containing their ingredient, so the researchers stop the experiment, concluding this is enough evidence that their product will sell the most. Is this a good experiment and conclusion? State reasons for your explanation, and what you would do differently.

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.)