(a) SUPERCALIFRAGILISTICEXPIALIDOCIOUS is a famous word that was made up into a song in the 1964 movie Mary Poppins. Identify how many letters of each alphabet there are and determine how many ways to arrange the letters in the word if: (i) (ii) (b) (i) the vowels must altogether be at the beginning or at the end. (Simplify but leave your answer in factorial notations.) no two I's are adjacent. (Simplify but leave your answer in factorial notations.) Give a recurrence relation for the number of different ways someone can pay a parking fee at a shopping mall using the slot-in machine with 10-sen, 20-sen and 50-sen coins in the amount of 10n sen if the order of how the coins are inserted matters. (ii) From your answer in (i), how many different ways can someone pay a parking fee of 80 sen? (c) Salbiah wants to put sixteen identical apples slices into six different lunch boxes. How many ways can she do this if: (i) each lunch box must have at least two apple slices? (ii) each lunch box will have at least one but not more than 5 apple slices?