In this problem we assume that h: U → {0, 1, . . . , m − 1} is a good hash function, that is, every key k has the same probability 1/m to map to any place in the table T of length m. (i) What is the probability that three pairwise distinct elements u1, u2, u3 ∈ U are mapped by the function h to the same place in the table (that is, h(u1) = h(u2) = h(u3))? (ii) We insert three elements into an empty hash table T using the hash function h. If collision is solved by chaining, what is the probability that T[0] and T[1] are empty?

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A: Please refer to the following step for the complete solution to the problem above.

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A: Introduction

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