A survey of 500 farmers showed that of the farmers, 128 grew wheat, 108 grew only corn, 93 grew only oats, 205 grew wheat, 63 grew wheat and corn, 52 grew wheat and oats, and 185 grew corn. Determine the number of farmers who a) grew at least one of the three, b) grew all three, c) did not grow any of the three, and d) grew exactly two of the three.

I’m confused on how to work the pie charts

Sum of the interior angles of a pentagon

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.)