an elevetor in a building starts with five passengers and stops at seven floor. In each passenger is equaly likely to get off at any floor and all the passengers leave independently of each other. What is thr probability that no two passengers will get off at the same floor.

Each person can select any of the seven floors.

Hence Number of All possibilities = 7^5 = 16807

(This is the number of possibilities when each person selects any floor)

If each passenger goes to a different floor:

We have to find permutations of 5 out of 7

Number of ways is 7*6*5*4*3 = 2520

(This is the number of possibilities when each person selects a different floor)

Probability = 2520/16807 = .15