A student is preparing for an upcoming exam. The professor for the course has given the class 20 problems to study from and plans to select 5 of the problems at random for use on the actual exam. Suppose that the student knows how to solve 17 of the 20 problems. Let X represent the number of problem the student answers correctly on the test.
(A) What is the probability distribution of X? Why? Be sure to specify the values of all necessary parameters.
(B) What is the probability that the student will get perfect on the test?
(C) What is the probability that the student will get at least 4 problems correct on the test?