Please help I suck at math :)

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.)

Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x â’ 1 , y = 0, x = 5; about the x-axis v = sketch the region. sketch the solid, and a typical disk or washer.

Caleb and emily are standing 100 yards from each other. caleb looks up at a 45° angle to see a hot air balloon. emily looks up at a 60° angle to see the same hot air balloon. approximately how far is the hot air balloon off the ground? a)44.2 yd. b)63.4 yd. c)73.2 yd. d)89.7 yd.