If f(x) and g(x) are given, explain how to find (f g)(x) and then how to find (g f)(x) . Choose the correct answer below. O A. To find (f g)(x) , the expression for f(x) should be substituted for x into g(x) . To find (gof f)(x) the expression for g(x) should be substituted for x into f(x) . O To find (f g)(x) , the expression for g(x) should be substituted for into f(x) . To find (g f)(x) the expression for f(x) should be substituted for x into g( x). To find (f g)(x) or (g f)(x) , multiply the expression for f(x) by the expression for g(x) .

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.)