The renewed interest in this old post, reminded me of a more recent event:
Question: In how many ways you can chose a committee of three students from a class of ten students?
My expected answer: which is 120.
Alternative answer 1:(Lior) There are various ways: you can use majority vote, you can use dictatorship (e.g. the teacher chooses); approval voting, Borda rule…
Alternative answer 2: There are precisely four ways: with repetitions where order does not matter; with repetitions where order matters; without repetitions where order matters; without repetitions where order does not matter,
Alternative answer 3: The number is truly huge. First we need to understand in how many ways we can choose the class of ten students to start with. Should we consider the entire world population? or just the set of all students in the world, or something more delicate? Once we choose the class of ten students we are left with the problem of chosing three among them.