A graph titled position versus time has a horizontal axis time (seconds) and a vertical axis position (meters). A straight line passes from 0 seconds, 0 meters to 5 seconds, 20 meters. Calculate the slope of the line on the graph using the formula: m = m = v subscript 2 - v subscript 1 over x subscript 2 minus x subscript 1. The slope of the line is m/s.

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.)