Hash Table Linked List Length

[Sius]

A hash table with chaining is required to hold 10000 records. Each record is indexed by the 2-character initials of the user's name, transformed into integers using the mapping: A=01, B=02,...,Z=26. Ideally, on average, no more than 8 comparisons should be made every time a search is requested.

For example, John Doe:

John Doe = JD

J = 10

D = 04

JD = 1004

The hash function (multiplication hash): h(k) = m(kA - kA)

k = 2-character initials as an integer (e.g, 1004)

A = 0.6180339887

m = 1000

In this case, how do you compute the average length of the linked lists, in the hash table, that is pointed to by the hash value slots?