In a local 8-ball league, players are issued a handicap based on their ability. the handicap is used to adjust scores between players of different ability levels. the better a player is, the lower his or her handicap will be. what type of correlation exists between the skill of a player and his or her handicap? a. no correlation exists between a player's skill level and handicap. b. a positive correlation exists between a player's skill level and handicap. c. a negative correlation exists between a player's skill level and handicap. d. there is not enough information to determine what type of correlation exists between a player's skill level and handicap.

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.)