Five persons entered the lift cabin on the ground floor of an 8-floor house. Suppose each of them can leave the cabin independently at any floor beginning with the first. The probability of all five persons leaving at different floors, is

Answer

`(.^(7)P_(5))/(7^(5))`

Explanation

In an 8-floor house, there are 7 floors above the ground floor.
Each person can leave the cabin at any of the seven floors, i.e., each person can leave the cabin in 7 ways. Thus, total number of ways into which 5 persons can leave the cabin is `7^(5)`. Now number of the ways of leaving the cabin by 5 person each at different floor is `.^(7)P_(5)`.
Hence, the required probability is `.^(7)P_(5)//7^(5)`.