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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. Find out the probability of all five persons leaving at different floors.

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The correct Answer is:
`(.^(7)P_(5))/(7^(5))`
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)`.
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