In the following, assume that all keys are distinct.

(a) Consider a hash table with m buckets that uses chaining for collision resolution. The table is initially empty. What is the probability that, after k keys are inserted, there is a chain of size k 1?

(b) Consider a hash table with m slots that uses open addressing with linear probing. The table is initially empty. A key k1 is inserted into the table, followed by key k2. What is the probability that inserting key k3 requires three probes?

Please give a complete answer.