In pottery class, ludolf made a cylindrical vase that is 32 cm tall. its base has a radius of 8 cm. he wants to paint the outside of the vase. how many square centimeters will ludolf have to paint? round to the nearest whole number. use 3.14 as an approximation for pi.

a. 6431 cm2

b. 1608 cm2

c. 1809 cm2

d. 2010 cm2

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.)