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Question 1 Suppose we throw it balls into m; bins, by choosing for each ball a bin uniforme and independently at random. The halls are labeled with distinct numbers from 1 to k and the bins with distinct numbers from 1 to m. 1f a) Let S i; {1, . . . , is}. What is the probability that all balls in S are thrown into the same bin? Express this probability in terms of |S| and m. (b) Give an upper bound for the probability that there exists a bin that contains three or more balls. Your upper bound should use the union bound, and be as small as possible. Explain and show all your calculations