Mr. stanton bought 121 feet of rope to repair a rope bridge. the ratio of the two pieces that he needs from the length he bought is 4 to 7. if he uses the entire length of rope, how long is each piece?

a
40 feet and 70 feet
b
42 feet and 79 feet
c
43 feet and 78 feet
d
44 feet and 77 feet

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.)