Harry, Ron and Hermione want to get to the Philosopher's stone before Professor Quirrell. In order to do so they need to pass through those obstacles. Below is the brief description of some of the characters in the story. Name Description Harry A wizard, 11 years old. Ron A wizard, the ultimate best friend of Harry. Hermione A witch, close friend of Harry and Ron. Professor Quirrell Defence Against the Dark Arts teacher at Hogwarts. Professor McGonagall Head of Giyindor house, the Transguration teacher at Hogwarts. Professor Snape Head of Slytherin house, Potions master at Hogwarts. Professor Dumbledore The headmaster of Hogwarts. ANSWER ALL QUESTIONS Question 1 |20 marks| Their first obstacle is to get past Fluffy, a three-headed dog. Harry decides to play some music to let the dog fell into sleep. The song that he plays consists of 60 musical notes and each note can be one of the seven solfeggio syllables (Do-Re-Mi-Fa-Sol-La-Si). (a) Find the number of songs that he can play if (i) the song must consist at least a \"Do\". [3 marks] (ii) the song must consist exactlyt two syllables. [4 marks] (b) Each head of Fluffy may attack people. When Fluffy attacks, a person may get either major or minor injuries. Let X be the total number of attacks at one time, and let Y be the total number of major injuries caused by the attacks. The joint probability function of X and Y is C(3x +y), x : 0,1,2,3, y : 0,1,2,3, x 2 y pony) = 0, othemise Find (i) E(Y | X >1) [6 marks] (ii) the variance of minor injuries caused by the attacks. [7 marks]