Four persons entered the lift cabin on the ground floor of a six floor office . if the 4 persons can leave the cabin at any one of the 5 floors , then find the number of ways in which this can be done

Answer

To solve the problem of how many ways 4 persons can leave a lift cabin at any of the 5 floors, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the Options for Each Person**:
Each of the 4 persons can leave the lift at any one of the 5 floors. This means that for each person, there are 5 choices available.

2. **Calculate the Total Combinations**:
Since the choices of the persons are independent of each other, we can use the multiplication principle of counting. This means we multiply the number of choices for each person:
- Person 1 has 5 choices (floors).
- Person 2 has 5 choices (floors).
- Person 3 has 5 choices (floors).
- Person 4 has 5 choices (floors).

Therefore, the total number of ways in which all 4 persons can leave the lift is calculated as:
\[ \text{Total Ways} = 5 \times 5 \times 5 \times 5 = 5^4 \]

3. **Calculate \(5^4\)**:
Now we compute \(5^4\):
\[ 5^4 = 625 \]

4. **Conclusion**:
Thus, the total number of ways in which the 4 persons can leave the lift at any of the 5 floors is **625**.

### Final Answer:
The number of ways in which the 4 persons can leave the cabin is **625**.