18. Stereo Store A stereo store sells three brands of stereo systems, brands A, B, and C. It can sell a total of 100
stereo systems per month. Brands A, B, and C take up,
respectively, 5, 4, and 4 cubic feet of warehouse space,
and a maximum of 480 cubic feet of warehouse space
is available. Brands A, B, and C generate sales com-
missions of $40, $20, and $30, respectively, and $3200
is available to pay the sales commissions. The profit
generated from the sale of each brand is $70, $210, and
$140, respectively. How many of each brand of stereo
system should be sold to maximize the profit?

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.)