After a parade, a group of volunteers is helping to pick up the trash along a 2-mile stretch of a road. The group decides to divide the length of the road so that each volunteer is responsible for cleaning
up equal-length sections.
1. Find the length of a road section for each volunteer if there are the following numbers of
volunteers. Show your reasoning.
a. 8 volunteers
b. 10 volunteers
c. 25 volunteers
d. 36 volunteers

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.)