SOLUTION: an elevator in a building starts with 6 people and stops at 8 floors.suppose ,all permutations of the passengers getting off at various floors are equally likely,find the probabili

We will get the probability of the complement event, where no more
than 1 person gets off at any floor, and then subtract that from 1:
 
Each of the 6 people has in mind one of those 8 floors as his or her 
exit floor.

We will get the denominator of the probability first:

Suppose the 6 people line up in a single file to enter the elevator.

Then 

We can choose the exit floor for the 1st person any of 8 ways
We can choose the exit floor for the 2nd person any of 8 ways
We can choose the exit floor for the 3rd person any of 8 ways
We can choose the exit floor for the 4th person any of 8 ways
We can choose the exit floor for the 5th person any of 8 ways
We can choose the exit floor for the 6th person any of 8 ways

That's 86 ways to choose their exit floors.  That is the denominator
of the probability, the total number of choices of exit floors
for all 6 people.

The numerator of the complement event is the number of ways
each has a different exit floor.  

We can choose the exit floor for the 1st person any of 8 ways
We can choose the exit floor for the 2nd person any of 7 ways
We can choose the exit floor for the 3rd person any of 6 ways
We can choose the exit floor for the 4th person any of 5 ways
We can choose the exit floor for the 5th person any of 4 ways
We can choose the exit floor for the 6th person any of 3 ways

That's 8·7·6·5·4·3 or 8P6 ways to choose their exit floors for
the complement event.  That is the numerator of the probability 
of the complement event.  So the probability of the complement
event is

= .0769042969

So the desired probability is 1 - .0769042969 = .9230957031

or in exact form 

Edwin