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

$\frac{{^nP}_m}{n^m}$

Choose 'm' floors out of 'n' floors = ${^nC}_m$ (one floor for each person)

Arrange 'm' person on these choosen floors in m! ways.

⇒ Favorable ways = ${^nC}_m . m!$, Total ways = n^m [as each person has m choice]

⇒ P(required) = $\frac{{^nC}_m.m!}{n^m}=\frac{{^nP}_m}{n^m}$