3. (25 points) To attend an elite school, students must pass a placement test. The test consists of 12 multiple-choice questions, each with one correct answer and four other incorrect answers. A student must answer 10 of the 12 questions correctly to pass the test. (a) If a student taking the test answers each question by selecting one of the five options at random, what is the probability that the student will pass the test? (b) Suppose that the student can successfully eliminate one incorrect answer from each of the 12 questions before selecting one of the four remaining options at random. In this scenario, what is the probability that the student will pass the test? (c) Suppose instead that the 12 questions are True-False questions so that there are only two options: one correct answer and one incorrect answer. If the student answers each of the 12 questions by selecting an answer at random from the two options, what is the probability that the student will pass the test?