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a math department has n professors and 2n courses, each professor teaching two courses each semester. how many ways are there to assign the courses

a math department has n professors and 2n courses, each professor teaching two courses each semester. how many ways are there to assign the courses in the fall semester? how many ways are there to assign the courses in the spring semester such that no professor teacher the same pair of courses in the spring as in the fall? if all the assignments are equally likely, what is the probability of this event?

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