Question:

7 passengers enter an elevator on the first floor of an 11-floor building.

Assume that the egress pattern to floors 2,3,....,11 is the same. What is the probability that all get off at different floors?

My Answer:

Number of objects to be arranged = 7passengers + (11floor - first floor - 1) = 16 objects

Possible arrangements = 16C7 = ways of egress

Ways of all get off at different floors = 9C2 ( 9 floors, 2 floors with no passenger gets out)

P(probability that all get off at different floors) = 9C2/16C7 = 0.00315 <---------Which is WRONG!!!!!

The correct answer is0.0605, but I have no idea on how to do it, I am so frustrated ...