A10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. if the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

a. the volume of the cylinder with height 10 is 60π60π cubic inches greater than the volume of the cylinder with height 6.

b. the volume of the cylinder with height 6 is 60π60π cubic inches greater than the volume of the cylinder with height 10.

c. the volume of the cylinder with height 10 is 60π60π cubic inches greater than the volume of the cylinder with height 6.

d. the volume of the cylinder with height 6 is 60π60π cubic inches greater than the volume of the cylinder with height 10.

e. the volume of the cylinder with height 6 is 240π240π cubic inches greater than the volume of the cylinder with height 10.

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.)