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.