Example 5.2. In a multiple choice examination, each question is supplied with 3 pos- sible answers of which one is the correct answer to the question. A student, who does not know any of the correct answers, is doing the examination by selecting answers at random. What is the probability that (a) out of the 5 questions answered the student has (i) exactly 3 correct answers, (ii) at least 3 correct answers; (b) (i) the third question answered is the first correct answer; (ii) at least 3 questions out of the 10 questions to be answered are needed to get the first correct answer; (c) the 5th question answered is the 3rd correct answer; (ii) at least 4 questions, out of the 10 questions answered, are needed to get the 3rd correct