Question: [ 12 points ] You put k keys into a hash table with m hash buckets . We assume that the hash function is good

[ 12 points ] You put k keys into a hash table with m hash buckets . We assume that the hash function is good enough that you can treat the destination of each key as independently uniformly random . What is the probability that there are no collisions at all , i.e. , that all keys end up in different positions of the array ? Show your work as you derive your answer . ( 5 ) [ 12 points ]

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