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.

Explanation

To solve the problem of finding the probability that all five persons leave the lift at different floors in an 8-floor building, we can follow these steps:

### Step 1: Determine the total number of ways the five persons can exit the lift.
Each of the five persons can choose any of the 8 floors to exit. Since their choices are independent, the total number of ways they can exit is given by:
\[ \text{Total ways} = 8^5 \]
This is because each person has 8 choices.
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