Todd is playing a carnival game in which a ball of 1 of 3 colors (red. green, or purple) comes out of the machine whenever he puts money into it. Red balls are worth 1 point; green balls are worth 5 points; purple balls are worth 10
points. He has 5 times as many red balls as green ones, and he has 1 more purple ball than he has green balls.
Currently, he has a total of 150 points. How many purple balls does he have?

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.)