Question

A lecturer is teaching a Discrrete Math course give a multiple choice quiz that has ten questions, each with four possible responses:a, b, c, d, what is th minimum number of students that must be in the class in order to guarantee that at least three answer sheets must be identical.....

Answer 1

Just a guess:
Each question can have 4 possible choice. You have 10 questions, total no. of combinations is 4x4x....x4 = 4^10

For at least two sheet must be identical, that is 4^10 answer sheet are not the same, so we need one more, then that would be 4^10 + 1

However, we need three answer sheets must be identical. The worst case is when we can only find two identical answer sheet in 4^10 + 4^10 answer sheets.So, to guarantee there are 3 identical answer sheets, we need 4^10 + 4^10 +1.

Not quite sure if my logic is right though :(