Question 50
In how many ways can we place 8 digits equal to 1 and 8 digits equal to $0$ on a $4 \times 4$ board so that the sums of the numbers written in each row and each column are all the same?
| 1 | 0 | 1 | 0 |
| :--- | :--- | :--- | :--- |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| :--- | :--- | :--- | :--- |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |