Ascience test, which is worth 100 points, consists of 24 questions. each question is worth either 3 points or 5 points. if x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 what does the solution of this system indicate about the questions on the test? the test contains 4 three-point questions and 20 five-point questions. the test contains 10 three-point questions and 14 five-point questions. the test contains 14 three-point questions and 10 five-point questions. the test contains 20 three-point questions and 8 five-point questions.

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.)