There are four chairs with two chairs in each row. In how many ways can four persons be seated on the chairs, so that no chair remains unoccupied?

Options

A. 6
B. 12
C. 24
D. 48

Answer

To solve the problem of seating four persons on four chairs arranged in two rows with two chairs each, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Arrangement**: We have 4 chairs in total, arranged in 2 rows with 2 chairs in each row. The chairs can be labeled as A1, A2 (first row) and B1, B2 (second row).

2. **Total Persons**: We have 4 persons to seat, and we need to ensure that all chairs are occupied.

3. **Calculate Total Arrangements**: The total number of ways to arrange 4 persons in 4 chairs can be calculated using the factorial of the number of persons (or chairs). This is given by:
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

4. **Consider Row Arrangement**: Since the chairs are arranged in rows, we need to account for the fact that the arrangement of chairs in rows does not change the overall arrangement of persons. Each arrangement of persons can be reflected in the rows.

5. **Divide by Row Arrangements**: There are 2 rows, and since the arrangement within each row does not change the overall arrangement of the persons, we need to divide by the number of ways to arrange the rows. The arrangement of 2 rows can be calculated as:
\[ 2! = 2 \]

6. **Final Calculation**: Thus, the total number of ways to seat the 4 persons such that no chair remains unoccupied is:
\[ \frac{4!}{2!} = \frac{24}{2} = 12 \]

### Conclusion:
The total number of ways to seat four persons on the four chairs, ensuring that no chair remains unoccupied, is **12**.