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 a. `(\ ^7P_5)/(7^5)` b. `(7^5)/(\ ^7P_5)` c. `6/(\ ^6P_5)` d. `(\ ^5P_5)/(5^5)`

Explanation

Since, if is an eight-storey building.
So, there are `7` possible options for them in `7` floors in total if ground floor is not considered.


Hence, total possible outcomes


`=7×7×7×7×7=7^5`


Thus, number of ways in which 5 persons can leave from seven floors differently
`= 7_(P_5)`


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