Grace and her friends are playing a game that uses two dice. Each die is a tetrahedron – a four‐sided shape with each side an equilateral triangle. Each side of the die contains one of the digits 1, 2, 3, or 4. pls. i rlly need answers. for an assignment.
a. Create the sample space of all possible outcomes if you were to roll the two dice
simultaneously. List the digit on the first die first and the digit on the second die
second (i. e. 1,1; 1,2; and so on.) (10 points)
b. What is the theoretical probability that the sum of the two numbers on a roll will
be five? (2 points)

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.)