Four persons entered the lift cabin on the ground floor of a six floor office , susppose 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 four persons can leave the cabin at different floors .

Answer

To solve the problem of how many ways four persons can leave a lift cabin at different floors in a six-floor building, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Floors**:
There are a total of 6 floors, but since the persons can only leave starting from the first floor, we have 5 available floors (1st to 5th).

2. **Choices for Each Person**:
- The first person can choose any of the 5 floors to exit.
- After the first person exits, there are 4 floors remaining for the second person.
- After the second person exits, there are 3 floors remaining for the third person.
- Finally, after the third person exits, there are 2 floors remaining for the fourth person.

3. **Calculate the Total Number of Ways**:
The total number of ways the four persons can leave the lift cabin can be calculated by multiplying the number of choices available for each person:
\[ \text{Total Ways} = 5 \times 4 \times 3 \times 2 \]

4. **Perform the Multiplication**:
- First, calculate \(5 \times 4 = 20\)
- Then, calculate \(20 \times 3 = 60\)
- Finally, calculate \(60 \times 2 = 120\)

5. **Conclusion**:
Therefore, the total number of ways in which each of the four persons can leave the cabin at different floors is **120**.

### Final Answer:
The total number of ways in which each of the four persons can leave the cabin at different floors is **120**.