Exercise 6. At 170E the instructor, who is an odd-duck and apparently doesn't believe in Covid, asks all of the n students in the class to shake hands with each other. Accordingly, the students walk about the classroom, shaking hands at random. (a) How many different pairs of students could shake hands? Call this number N. (b) What is the probability that after exactly N hand shakes, every student has shaken every other student's hand exactly once