Triangle abc, with vertices a(3, 0), b(2, 4), and c(4, 2), undergoes a transformation to form triangle a′b′c′, with vertices a′(3, 0), b′(2, -4), and c′(4, -2). the type of transformation that triangle abc undergoes is a . if triangle a′b′c′ undergoes a transformation to form triangle a″b″c″, with vertices a″(-3, 0), b″(-2, -4), and c″(-4, -2), then the type of transformation that triangle a′b′c′ undergoes is a .

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.)