The Johnsons are moving from Aviemore in Scotland to live at their new house in Sunderland. They wish to move their large garden shed which measures 5.3m (length), 3.0m (width) and 1.5m (height). At the new residence, they require the shed placed so that its length is parallel to one of the rear garden walls. The garden is a square of area 27.3 m2. Will the shed fit in the garden as required? Show your working

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.)