The six sides of a number cube are labeled 1, 2, 3, 4, 5, and 6. You flip a coin and roll the number cube. What is the theoretical probability that the coin lands on tails and you roll a number less than 3? Write your answer as a fraction. A) 1 over 12.
B) 1 over 6.
C) 4 over 12.
D) 6 over 12.

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.)