Question

1. For all parts of this question, working is required, including combinatoric/factorial notation as needed as well as final answers.

a) (*) A gym has the following group fitness sessions:

 Zoomba

 Body conditioning

 Weight lifting

 Boxing

 Yoga

A member can attend one session at most once a day (i.e., once a member has attended Zoomba classes, s/he cannot attend it again that day). The duration of sessions is also unimportant, however, for example, doing Zoomba before boxing and doing boxing before Yoga should be considered different. We are interested in working out the different ways people can attend the gym sessions.

i. How many different attending (engagement with the fitness sessions) patterns can be formed from those five fitness sessions?

ii. How many patterns contain only three types (e.g., yoga – body conditioning - Zoomba)?

iii. How many patterns with at least four different activities start with Yoga?

b) (*) You are at an ice cream shop, there are six different flavours you can choose from. i. How many ways you could select the flavours? Explain in a sentence how you calculated your answer.

ii. How many ways could select three flavours only? (1 mark)

c) (**) You collected 12 supermarket gifts/collectables (either mini tree house books from Coles or ooshies from Woolworths), all are different. You would like to put those in groups and place those to different locations around the house. i. If there are four different locations around the house, and three collectables are to be placed at each location, how many different ways can the collectables be arranged?

ii. Show a second approach to your answer to i. [1 mark]

d) (**) [3 marks] You prepare a schedule of your physical exercises for the next fortnight (14 days). You don’t do physical exercise more than once a day. If you have 10 PE sessions planned, explain using the counting principles covered in class how this means you will do PE on consecutive days at least once in the next fortnight.

Answer 1