In: Math
8. Adam, Bonnie, Chuck, Dave and Elaine are engineers from different companies attending a professional conference at the University of Arizona in Tucson. There are seven hotels near the campus. Each engineer will stay at a randomly picked hotel. a. What is the probability that they will all stay at the same hotel? b. What is the probability that they will all stay at different hotels? c. Adam has a crush on Bonnie, what is the probability that they will stay at the same hotel? d. What is the probability that exactly two of the five engineers will stay at the same hotel with no one else staying at a same hotel?