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 combinatric/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, so once you have completed your freestyle laps, you do not repeat frees for each lap type is unimportant, that is, 4 laps of freestyle followed by same as 3 laps of freestyle followed by 4 laps of backstroke.

i. How many different lap type patterns can be formed from those six types?

ii. How many patterns contain only three types (e.g., freestyle - arms only- one arm only?

iii. How many patterns with at least four different types start with lops?