Consider three classes, each consisting of n students. From this group of 3n students, a group of 3 students is to be chosen.
(a) How many choices arc possible?
(b) How many choices arc there in which all 3 students are in the same class?
(c) How many choices are there in which 2 of the 3 students are in the same class and the other student is in a different class?
(d) How many choices are there in which all 3 students are in different classes?
(e) Using the results of parts (a) through (d), write a combinatorial identity.
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