5. a small toy company makes only cars and trucks. the profit made on cars is $2 each and the profit made on trucks is $3 each. to stay in business, the company must make at least $500 profit each week. the company only has the resources to make up 200 total cars and trucks each week. a) write a system of inequalities that represent possible combinations of toys that the company can make and the amount of profit they will earn. be sure to define your variables. b) can they stay in business? if so, how? (provide evidence)

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.)