Which statement is not true about the ratio of the leg lengths of increment δlrm and increment δjsk? a. the slope of the hypotenuse is represented by the ratio of the leg lengths. b. the ratios of the lengths of the legs are similar, which means the triangles are similar. c. the triangles are similar because the ratios of the lengths of the legs are proportional. d. the ratios of the lengths of the legs determine that the triangles are similar, and the hypotenuse of similar triangles will have the same slope.

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.)