Consider a hash table with n buckets, where external (overflow) chaining is used to resolve collisions. The hash function is such that the probability that a key value is hashed to a particular bucket is 1/n. The hash table is initially empty and k distinct values are inserted in the table. What is the probability that bucket number 1 is empty after the K insertions?
What is the probability that no collision has occurred in any of the K insertions?
What is the probability that first collision occurs at the Kth insertion?

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