Three people get into an elevator at the ground floor of 12

Three people get into an elevator at the ground floor of 12 story building. Assuming each person is equally likely to get off at each floor, what is the probability that they get off at the same floor?

Solution

There are 12^3 ways to get off at any floor they want.

Now, there are 12 ways to get off all at the same floor.

thus,

P(same floor) = 12 / (12^3) = 1/144 or 0.006944444 [ANSWER]