Question: Suppose m professors randomly choose from n time slots to hold their final exams. If two professors pick the same time slot, we say that

Suppose m professors randomly choose from n time slots to hold their final exams. If two professors pick the same time slot, we say that they are in conflict. (If three professors all pick the same time slot, that gives three pairs of professors in conflict.) What is the expected number of pairs of professors in conflict? Your answer should depend on m and n

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