A history teacher has given her class a list of seven essay questions to study before the next test.
The teacher announced that she will choose four of the seven questions to give on the test, and each student will have to answer three of those four questions.
a. In how many ways can the teacher choose four questions from the set of seven?
b. Suppose that a student has enough time to study only five questions. In how many ways can the teacher choose four questions from the set of seven so that the four selected questions include both questions that the student did not study?
c. What is the probability that the student in part b will have to answer a question that he or she did not study? That is, what is the probability that the four questions on the test will include both questions that the student did not study?