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!  

OK, I apologize for the wrong answer here. I give the correct solution now:
$$
P(S)=\frac{13!}{7!14^6}
$$
This is because the first person can go to any floor, and the other 6 can select any floor apart from the one already taken, the probability of which is $\frac{14-(k-1)}{14}$.
