There are 5 students in a music class and for them there are 5 seats in a row. On examination day, all five students are randomly allotted the five seats. Let denote the event that and do NOT sit adjacent to each other on examination day. (i=1,2,3,4)
What is the probability that all occur simultaneously on examination day?
If the probability is of the form , where and are coprime positive integers, find