An elevator starts with m passengers and stops at n floors (m≤n). The probability that no two passengers alight at the same floor is 

$\frac{^nP_m}{n^m}$

Since a person can alight at any one of n floors. Therefore, the number of ways in which m passengers can alight at n floors is $n × n × n× .........×n = n^m .$

m - times

The number of ways in which all passengers can alight at different floors is ${^nC}_m ×m ! = {^nP_m}$.

Hence, required probability $= \frac{^nP_m}{n^m}$