A multiple-choice quiz consists of 12 independent questions, each having four options with exactly one correct answer. A student, who does not know any of the answers, decides to guess randomly on every question.
(i) Find the probability that the student answers exactly 5 questions correctly.
(ii) Calculate the probability that the student answers at least one question correctly.
(iii) Determine, with justification, the number of correct answers that is most likely to occur when the student guesses on all 12 questions.