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. Find the total number of ways in which each of the five persons can leave the cabin (i) at any one of the 7 floors (ii) at different floors.

Explanation

To solve the problem step by step, we need to break it down into two parts as given in the question.

### Part (i): Total number of ways in which each of the five persons can leave the cabin at any one of the 7 floors.

1. **Understanding the scenario**: We have 5 persons and 7 floors (from 1st to 7th floor). Each person can independently choose any of the 7 floors to exit the lift.

2. **Calculating the choices for each person**:
- The first person has 7 choices (floors 1 to 7).
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