Six stand-up comics, a, b, c, d, e, and f, are to perform on a single evening at a comedy club. the order of performance is determined by random selection. find the probability that:

(a) comic f will perform fourth
(b) comic d will perform fourth and comic b will perform second.
(c) the comedians will perform in the following order: f, d, b, a, c, e.
(d) comic c or comic e will perform last.

You're locked out of your house. the only open window is on the second floor, 25 feet above the ground. there are bushes along the edge of the house, so you will need to place the ladder 10 feet from the house. what length ladder do you need to reach the window?

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.)

Which point-slope form equation represents a line that passes through (3,-2) with a slope of -4/5