Mars inc. says that until very recently yellow candies made up 20% of it's milk chocolate m& m's, red another 20%, and orange, blue, and green 10% each. the rest are brown. on his way home from work the day he was writing these exercises, one of the authors bought a bag of plain m& m's. he got 29 yellow ones, 23 red, 12 orange, 14 blue, 8 green, and 20 brown. is this sample consistent with the company's stated proportions? test an appropriate hypothesis and state your conclusion.

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.)