Based on the provided information about the characteristic roots and the right hand side function g(t), determine the appropriate form of a particular solution to be used with the undetermined coefficient method.

(a) r1=-2i; r2=2i g(t)=2sin(2t) + 3cos(2t)
(b) r1=r2=0; r3=1 g(t)= t^2 +2t + 3

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.)