A swimming team consists of 4 swimmers

Question 1 [25 marks]:
A swimming team consists of 4 swimmers. The following table tabulates the time it took for
each swimmer to swim a standard length (50 meter) with different technique at practice.

Technique | Free style Breast stroke Butterfly Back stroke
Swimmer () (2) (3) (4)
Andrew 44 44 41 43
Bernard 41 47 42 42
Chester 40 43 44 46
Daniel 46 44 45 48

The team is entering a relay team contest, where in a team each of the swimmers must swim
50 meters using a different technique listed in the table. Using brute force strategy, assign
the four techniques to the 4 swimmers such that the total time for the team is optimal.

(a) How many possible assignments (solutions) in total in using pure brute force (that is,
brute force without considering any constraint).
[5 mark]
(b) How many possible assignments (solutions) in total in using brute force with the
constraint that each swimmer must use a different technique taken into consideration
[5 mark]
(c) Show all the possible combinations of assigning the techniques to the four swimmers
according to Q1(b) and indicate the total time for each of the assignments.
[10 mark]
(d) Which combination(s) of swimming technique yields the lowest (optimal) total team time?

[5 mark]