A multiple choice has 3 questions, each with four possible answers:?
Assuming that a candidate can select only 1 out of the 4 options, and answering all questions is compulsory, it can be noted that each question can be answered in 4 ways. \therefore the total number of ways of answering the given question paper = 4^{3} = 64 ways Now, it may so happen that if the total number of candidates appearing in the exam \leq 64, each candidate answers differently. However, if there are 64 + 1 = 65 candidates appearing for the exam, and there are only a possible set of 64 answers to select from, at least two candidates have to answer identically.