Question 143
On the following board $4 \times 4$ 4 towers, 4 horses, 4 bishops and 4 pedestrians must be placed so that in each row and in each column the pieces placed are different, as in the example:
| $B$ | $T$ | $P$ | $C$ |
| :--- | :--- | :--- | :--- |
| $P$ | $B$ | $C$ | $T$ |
| $T$ | $C$ | $B$ | $P$ |
| $C$ | $P$ | $T$ | $B$ |
Pawns are rebellious and decided to stay in the following positions:
| | | $P$ | |
| :--- | :--- | :--- | :--- |
| $P$ | | | |
| | | | $P$ |
| | $P$ | | |
Calculate the number of modes in which the other parts can be placed.
| $B$ | $T$ | $P$ | $C$ |
| :--- | :--- | :--- | :--- |
| $P$ | $B$ | $C$ | $T$ |
| $T$ | $C$ | $B$ | $P$ |
| $C$ | $P$ | $T$ | $B$ |
Pawns are rebellious and decided to stay in the following positions:
| | | $P$ | |
| :--- | :--- | :--- | :--- |
| $P$ | | | |
| | | | $P$ |
| | $P$ | | |
Calculate the number of modes in which the other parts can be placed.