A student is studying for an exam, and a couple of weeks before the exam, the instructor gives him a list of all possible questions that may appear on the exam. Let this number of questions be W. On the exam, the instructor selects from these some questions to put on the exam. Let this number of questions be X.

Then, the instructor gives the student a choice from this number of X questions, of how many he must answer. Let this number of questions be Y. Before the exam, the student studies Z number of questions.

where W>X>Y

Find a function which yields (for every possible value of Z) the probability that this student will find himself dealing with at least one question he hasn't studied for.