A class has 50 students in total. Each student receives one of the letter grades: A, B, C, D or F, with probabilities 0.1, 0.2, 0.3, 0.3, and 0.1 respectively.

A class has 50 students in total. Each student receives one of the letter grades: A, B, C, D or F, with probabilities 0.1, 0.2, 0.3, 0.3, and 0.1 respectively. Students receive grades independently of each other. Let X1, X 2, X 3, X 4, X5 be the number of students that receive an A, B, C, D, and F respectively. (Final answers can be left in simplied fraction or factorial/permutation form). a) (2 marks) Find the probability that there are 10 A's, 15 3'5, 17 CS, 5 D's and 3 F 's. b) (2 marks) Find the probability that there are a total of 25 students with A's or B's. c) (2 marks) Find the probability that there are a combined 25 students with A's or B's and there are a combined 22 students with CS or D's. d) (2 marks) Given that there are 10 students with A's, what is the probability that there are 3 students with F's? e) (2 marks) Given that there are 10 students with A's, What is the expected number of students with F's