A probability question: a building and an elevator. Suppose that 7 people waiting for an elevator in a building with 14 flours.
Q: What is the probability that every person get out in different flour?
My attempt:
There is $14 \cdot 13 \cdot 12 \cdot \ldots \cdot 7$ ways to divide these 7 people in different flours. But what the total possibilities?
Thanks!  

The 7 people are waiting on one of the floors (probably the main floor), leaving 13 floors for them to possibly go to on the elevator.
The first person can go to any of the 13 possibilities, the second to any of the remaining  12, the third to any of the remaining 11, and so on...
So, the desired probability P is:$$P=\frac{13}{13}\times \frac{12}{13}\times \frac{11}{13}\times \frac{10}{13}\times \frac{9}{13}\times \frac{8}{13}\times \frac{7}{13}$$
If we assume 14 floors and another location to await an elevator as in the comment of Andre below, the desired probability P is:$$P=\frac{14}{14}\times \frac{13}{14}\times \frac{12}{14}\times \frac{11}{14}\times \frac{10}{14}\times \frac{9}{14}\times \frac{8}{14}$$
