The letters of the word DISTINCTION are to be arranged. (a) How many different arrangements of all the letters are possible? [4 marks] (b) How many of these arrangements begin and end with the letter I? [4 marks] (c) How many of the arrangements in (a) have all three letters I together? [4 marks] (d) Find the probability that a randomly chosen arrangement from (a) has all three letters I together. [3 marks]