Mr. Martin’s math test, which is worth 100 points, has 35 problems. Each problem is worth either 5 points or 2 points. Let x = the number of questions worth 5 points.
Let y = the number of questions worth 2 points.
x + y = 35,
5x + 2y = 100
How many problems of each point value are on the test?
A. 10 problems worth 5 points and 25 problems worth 2 points
B. 15 problems worth 5 points and 20 problems worth 2 points
C. 20 problems worth 5 points and 15 problems worth 2 points
D. 25 problems worth 5 points and 10 problems worth 2 points

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.)