Tyler simplified the expression x Superscript negative 3 Baseline y Superscript negative 9. His procedure is shown below. x Superscript negative 3 Baseline y Superscript negative 9 = StartFraction 1 Over x cubed EndFraction times StartFraction 1 Over y Superscript negative 9 EndFraction = StartFraction 1 Over x cubed y Superscript negative 9 EndFraction What is Tyler’s error? Both powers should be in the numerator with positive exponents. Both powers should be in the denominator with positive exponents. The power x cubed should be in the numerator and the power y Superscript 9 in the denominator. The power y Superscript 9 should be in the numerator and the power x cubed in the denominator.

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.)