Question

1. Our student clubs are being particularly active. The aquatics club in particular is in training for an upcoming competition. For all parts of this question, working is required, including combinatoric/factorial notation as needed as well as final answers. a) * [2 + 1 + 2 = 5 marks] During training, there are several different types of laps that can be swum: freestyle arms only freestyle one arm only, left then right torpedo/kickboard (straight kicking legs only) backstroke breaststroke Assume that each type is undertaken at most once in a training session, over contiguous laps (i.e., so once you have completed your freestyle laps, you do not repeat freestyle). The number of laps for each lap type is unimportant, that is, 4 laps of freestyle followed by 2 laps of backstroke is the same as 3 laps of freestyle followed by 4 laps of backstroke. b) ** [2 + 1 = 3 marks] The club is starting to look at putting together some relay teams. There are 15 swimmers nominating for this opportunity. i. If there are three different races, and a team of 5 needs to be nominated for each race, how many different teams can be formed? ii. Show a second approach to your answer to 1.

Answer 1

fa) ent