To decide what to eat at a restaurant, frank closes his eyes, places his finger on the menu, and orders whichever dish he places his finger on. he chooses one salad, one main course, and a dessert. if there were 10 possible dishes for each selection, how many possible combinations could he have chosen other than the one he selected?

Three numbers x, y, and z are in the ratio 2: 7: 8. if 12 is subtracted from y, then three numbers form a geometric sequence (in the order x, y–12, z). find x, y, and z. there are 2 sets.

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.)

You coordinate volunteers for litter cleanup in local parks. your spreadsheet lists drivers and the number of seat belts in each driver’s car. the spreadsheet calculates the number of drivers (d) and the total number of seat belts (s). you want to know the maximum number of volunteers, besides drivers, that can be transported to the park in a single trip given that each person must have a seat belt of their own.