Question 1 (20 marks) S=9 (a) In a student union selection, there are 3 candidates for the chairperson, 4 candidates for the vice- chairperson, 5 for the treasurer, 2 for secretary and S for recreational convener. How many ways can these five official committee positions be filled? [5 marks] (b) Find the number of ways to rearrange the letters "professional". [5 marks] (c) Given that P(A) = 0.3, P(B) = 0.6 and P(AB) = 0.8, find P(B|). [5 marks] (d) A box contains 9 red, 7 green and 4 blue balls. Two balls are selected at random without replacement. Find the probability that the selected balls are of different colour. [5 marks]