(b) A password will be formed using the letters in the word STATISTICS. Calculate all possible number of passwords in each of the following cases. (i) The letter in the centre is A. (3 marks) (ii) No vowel is next to another vowel. (3 marks) 5 letters are chosen from the word STATISTICS. (iii) Calculate the number of passwords which contain 2 T's and 1 A. (4 marks) (c) You are asked to select one of the four doors to open. There is a large prize behind one of the doors and if you select that door, you win the prize. After you select a door, the game show host opens one of the other doors (which he knows is not the winning door). The prize is not behind the door and he gives you the opportunity to switch your selection. Should you switch? Explain the reason on your decision. (5 marks) (Total: 20 marks)