Auniversity student earned grades 84, 78, 84, and 72 on his four regular tests. he earned a grade of 78 on the final exam and 86 on his class projects. his combined homework grade was 87. the four regular tests count for 40% of the final grade, the final exam counts for 30%, the project counts for 10%, and the homework counts for 20%. what is his weighted mean grade? round to one decimal place.

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.)