Seven persons are staying at a hotel. The hotel has twenty-five floors, each with the same number of rooms. Each of the seven persons has been randomly assigned to one of the rooms in the hotel.
a. What is the probability that at least two people have rooms on the same floor? Show and explain how you calculate the answer.
b. Suppose you are one of the seven people. What is the probability that at least one of the other six persons has a room on the same floor as you? Assume there are at least 6 rooms on each floor of the hotel. Show and explain how you calculate the answer.
c. Explain qualitatively why the answer to part b. is smaller than the answer to part a. In other words, give an intuitive argument or reason for the difference in probabilities