Posted by raj on .
A man is visiting a village where each person either always tells the truth or always lies. There are 5 villagers standing in a row, and the man asks each of them how many of the 5 men standing in the row always tell the truth. Each villager gives an integer answer from 0 to 5 (inclusive). How many possible multisets of answers could the man receive from the villagers?
Details and assumptions
A multiset is a set in which the elements are allowed to be repeated, e.g. {1,1,2,2}. This distinction is made because a set, by definition, should contain distinct elements. The multisets {1,2,2} and {1,1,2} are distinct multisets, but come from the same set {1,2}.
Changing the order of the villagers' answers does not change the set of answers received. I.E. the multiset {1,2,3,5,5} is the same as the set {5,3,2,1,5}.

maths 
exactly,
Only a hint: do a case by case analysis. You need N observation tho