Suppose n students are each independently assigned to a birthday in date 1, date 2, to date 365 uniformly at random.

Let T_n be the random variable equal to the number of unordered triples of students (sets of 3 different students) with the same birthday.

(a) Show that if n 120 then ET_n > 1.

(b) How large must n be to ensure that there are 3 students who share the same birthday which P(T_n 1) = 1?

Find the least such n.