I have got stuck on this question, is anyone able to help me please (any help is welcome):

Given an alphabet of 26 letters, how many sets of initials can be formed if every person has one surname and

i) exactly 2 given names

ii) at most 2 given names

iii) at most 3 given names

iv) The conclusion is that in a town of 20000 inhabitants then either some people have the same set of initials or at least x have more than 3 initials. How large is x?

Many thanks to anyone who has any advice.