A university offers 8 courses, numbered C1, C2, ..., C8. There are 40 students, and each takes three (different) courses, chosen at random from C1,..,C8, independent of ••.. choices of other students....

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Extracted text: A university offers 8 courses, numbered C1, C2, ..., C8. There are 40 students, and each takes three (different) courses, chosen at random from C1,..,C8, independent of ••.. choices of other students. 1. What is the expected number of students enrolled in course C1? 2. Are the events “Alice takes C1" and "Alice takes C2 independent? (Alice is one of the students). Prove your answer correct. 3. What is the probability that Alice and Bob have at least one course in common? (Bob is another student.)