April Challenge Problem Little Party... Question not clear

doubt
long_challenge

#1

I have been trying to ask my doubts through comments section since atleast 30-35 hours but no one responds…
Here are my doubts

  1. is it possible that a party was of form ABC for n=3 , i.e. all were in good mood ?
  2. Also what will be the answer if all possible combinations of Parties existed ?.. is it 0 or 1 or something else?

Plss don`t post answer in any form , not even anything close to answer . Just make the problem clear so everybody has a fair chance to solve it .
Thanks…


#2

if all possible parties are there, then answer should be 0. Sure about this part.
And ABC is possible, as from what I get from reading the problem.