In how many ways can 5 ladies draw water from 5 taps, assuming that no tap remains unused?

Explanation

To solve the problem of how many ways 5 ladies can draw water from 5 taps, ensuring that no tap remains unused, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Problem**: We have 5 ladies and 5 taps. Each lady must use a different tap, meaning that no tap can be used more than once.

2. **Assign Options for Each Lady**:
- The first lady has 5 taps to choose from.
- Once the first lady has chosen a tap, the second lady has 4 taps left to choose from.
- The third lady will then have 3 taps remaining.
- The fourth lady will have 2 taps left.
- Finally, the fifth lady will have only 1 tap to choose from.

3. **Calculate the Total Number of Ways**:
- The total number of ways can be calculated by multiplying the number of options available for each lady:
\[ \text{Total Ways} = 5 \times 4 \times 3 \times 2 \times 1 \]

4. **Recognize the Factorial**:
- The expression \(5 \times 4 \times 3 \times 2 \times 1\) is known as \(5!\) (5 factorial).
- Therefore, we can write:
\[ \text{Total Ways} = 5! = 120 \]

5. **Conclusion**:
- Thus, the total number of ways in which 5 ladies can draw water from 5 taps, ensuring that no tap remains unused, is **120**.