Let statements p, q, r, and s be as follow:
p: angle a and angle b are a linear pair.
q: angle a and angle b are supplementary angles.
r: angle a and angle b are adjacent angles.
s: angle a and angle b are adjacent and supplementary angles.
substitute for p, q, r, or s, and write the statement below the way you would read it.
p > q
angle a and angle b are supplementary if and only if angle a and angle b are a linear pair
if angle a and angle b are a linear pair, then angle a and angle b are supplementary angles
if angle a and angle b are supplementary, then angle a and angle b are a linear pair
angle a and angle b are a linear pair if and only if angle a and angle b are supplementary

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.)