Areflection of shape i across the y-axis, followed by a < 90 degree clockwise rotation, 90 degree counterclockwise rotation, 180 degree rotation around the origin.> and then a translation left 6 units and down 4 units confirms congruence between shape i and shape ii. alternatively, a < 90 degree clockwise rotation, 90 degree counter clockwise rotation, 180 degree rotation around the origin> of shape ii about the origin, followed by a reflection across the y-axis, and then a translation right 4 units and up 6 units confirms congruence between shape ii and shape i. which one?

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.)