Consider a room with 20 desks, each numbered from 1 to 20. The desks are arranged in a circle, so the desk numbered 20 is in between the desks numbered 1 and 19. Three students arrived one by one into an empty room and each chose from one of the empty desks to be seated with an equal chance given for each empty desk. Answer the following questions explaining how you derived your answer. 1) What is the probability of these three students sitting at the last three desks (i.e., the desks numbered 18, 19, and 20). 2) What is the probability of these three students sitting next to each other?