Write the recursive and the explicit formulas for the following real life problems: 3. Adam and Eve had two children, and let's say those children had two children
each, and the pattern continued so that every generation has two children each.
a) Write a table of values for the generation number vs. the total number of
children.
b) Write a recursive rule representing the number of children at each generation.
c) Write the explicit rule representing the number of children at each generation.
d) How many children will there be in the 10th generation?
e) How many generations would it take for there to be more than one thousand
children?

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.)