Jake just learned to identify the difference between an oak tree and a maple tree. He was curious about the concentration of these trees in his neighborhood, so he went out and identified several trees that were either by the pond or in the field. Unfortunately, he smudged his data tables and can’t read some of the values. The absolute and relative frequency tables below show Jake’s salvaged data. Can you help him figure out the rest? Fill in the missing values from each table.

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.)