Exercise 1. The mathematics department demands that the chair of the dissertation committee must be a mathematician in order to keep the physicists in check. What? How arrogant! But, there is no other choice if a dissertation committee has to be assembled in time. As usual, physicists have to swallow their pride in order to keep peace. Yes, they are just a bunch of you know what in the mathematics department! For comic relief, can you figure out how many ways can this hapless graduate student can choose among his beloved professors if the chair of the committee must be a mathematician, and the rest of the committee can be a mix of mathematicians and physicists?
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