Suppose n students are each independently assigned a birthday in {1, ..., 365}, uniformly a random. Let Tn be the random variable equal to the number of unordered triples (i.e., sets of three distinct students) of students with the same birthday. (a) Show that if n > 120 then ETn 2 1. (b) How large must n be in order to guarantee that there are three students who share the same birthday, i.e. P(T, >1) = 1? %3D Find the least such n.

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