The amount of a sample remaining after t days is given by the equation p (t) = a (1 / 2 )^ t / h, where a is the initial amount of the sample and h is the half-life, in days, of the substance. a sample contains 60% of its original amount of fermium-257. the half-life of fermium-257 is about 100 days. about how old is the sample?
a. 52 days
b. 60 days
c. 74 days
d. 136 days

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.)