Q4. The Faculty of Math is assigning 10 graduate students, including Alice and Bob, to proctor exams. Each graduate student will be randomly assigned to proctor one of three courses. . Math 103 will receive 3 of the 10 graduate students. . Math 104 will receive 2 of the 10 graduate students. . Math 106 will receive 5 of the 10 graduate students. (a) Determine, with justification, the number of ways the graduate students can be assigned. (b) Determine, with justification, the number of ways the graduate students can be assigned with Alice and Bob both being assigned to Math 103. (c) What is the probability that Alice and Bob will be assigned to proctor the same course? Q5. A book publisher evaluates 10 different textbooks by sending them to a number of teachers. (a) If they ask the teachers to list their 5 favourite books in order, how many different lists are possible? (b) If they ask the teachers to select their 5 favourite books, how many different selections are possible? (c) The 10 textbooks consist of 5 different algebra textbooks, 3 different calculus textbooks, and 2 different statistics textbooks. (i) If they ask teachers to list their 5 favourite books, determine, with justification, how many different lists include all three calculus textbooks. (ii) If they ask teachers to select their 5 favourite books, determine, with justification, how many different selections include all three calculus textbooks