In a very long toy train, the first and last cars were blue. After each blue car (except the last one), there were two yellow cars. After
each pair of yellow cars, there was a red car. After each red car,
there was a blue car. The first five train cars are shown in the
picture. Oleg picked a car and recolored all cars in front of it green.
Then Joyce picked a car and recolored all cars behind it green.
What is the least possible number of non-green cars in the
recolored toy train if it contains 7 more yellow cars than blue cars?

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.)