Michael has decided to plant grapes in the garden behind his house. his neighbor vincent has grown grapes successfully for a long time and has given michael advice about how to plant vines. vincent told him to plant them three meters apart in rows that are three meters apart. he also told him to leave at least three meters between each vine and the edge of the garden. michael has measured the size of his garden and learned that it’s a rectangle with sides of 25 meters and 35 meters. how many vines should michael buy?

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.)