Five persons entered the lift cabin on the ground floor of an `8` floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of al `5` persons leaving at different floor is

Options

A. a) `(7_(P_5))/(7^5)`
B. b) `(7^5)/(7_(P_5))`
C. c) `6/(6_(P_5))`
D. d) `(5_(P_5))/(5^5)`

Answer

a) `(7_(P_5))/(7^5)`

Explanation

There is `8`-storey building. There are `(8-1)=7` possible options for them as ground floor not taken


Total sample space `=7 times 7 times 7 times 7 times 7=7^5`


No’s of ways in which `5` persons can leave from different floors = 7_(P_5)


Required probability `=(7_(P_5))/(7^5)`


Hence, correct option is a)