1. Two people have $10 to divide between themselves. Each person names a number (nonnegative integer) no more than 10. If the sum of the two numbers is at most 10, each person gets the named amount of dollars, and the rest of the money is destroyed. If the sum exceeds 10, and the numbers are different, the person who has named the smaller number, receives the corresponding number of dollars, and the second person receives the rest. If the sum exceeds 10, and the numbers are equal, each person receives $5. Determine the be

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.)