Seventy students have registered their intention to participate in the behavioral economics course. For each of the five problem sets, forty-eight students will be selected at random to have their work graded, the random draws will be independent.

(a) Calculate the probability that a particular student will not be selected for any of the five problem sets.

(b) Calculate the probability that a particular student will be graded for exactly one of the five problem sets.

(c) A student is not selected to be graded for the first problem set, calculate the probability that the student is not graded for any problem set conditional on this event.

(d) A student decides to hand in three of the five problem sets, calculate the probability that the student was selected to be graded for the two problem sets that were not handed in and not for the three that were.