Nina made two investments: Investment \text{A}Astart text, A, end text has a value of \$50$50dollar sign, 50 at the end of the first year and increases by 8\%8%8, percent per year.
Investment \text{B}Bstart text, B, end text has a value of \$60$60dollar sign, 60 at the end of the first year and increases by \$3$3dollar sign, 3 per year.
Nina checks the value of her investments once a year, at the end of the year.
What is the first year in which Nina sees that investment \text{A}Astart text, A, end text's value exceeded investment \text{B}Bstart text, B, end text's value?

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.)