The grand cooking school of Tarator offers the three courses Riba, Meso and Sladki. Applicants choose one of the three courses to apply for and there always are a very large number of applicants to all three courses. (a) Assume that Tarator admits a total of n = 33 students and that the proportion of applicants applying to each of the three courses is the same. What is the probability that each course has exactly the expected number of participants given that participants are selected with equal chances of admission independently of their chosen course? [3] (b) What is the probability that more than half of the students will end up on the Meso course? You manage to convince the head of Meso, Miss Skara, that an approximate answer will be sufficient. [5] (c) Mr Palamudov, the head of Riba, is pleased that the number of students on his course has gone up. Explain why this is likely to result in fewer students on Miss Skara's course and compute the correlation of the two student numbers. Mr Palamudov suggests that doubling the size of the school would help average things out more - do you agree? Discuss quantitatively. In your discussion you should comment on the correlation as well as the proportion of students on any one course. Are the answers obtained using these two measures contradictory? How will this develop for even larger departments? [7]