Assume that n random positions of a tablesize-element hash table are occupied, using hash and rehash functions that are equally likely to produce any index in the table. The hash and rehash functions themselves are not important. The only thing that is important is they will produce any index in the table with equal probability. Start by counting the number of insertions for each item as you go along. Use that to show that the average number of comparisons needed to insert a new element is (tablesize + 1)/(tablesize-n+1). Explain why linear probing does not satisfy this condition.