Five. (25 points) As shown in Figure 5, place 3 identical coins sequentially into a $4 \times 4$ square grid (each square can only hold 1 coin). Find the probability that any two of the 3 coins are not in the same row or column.

Place the above text into the requested format:

Five. (25 points) As shown in Figure 5, place 3 identical coins sequentially into a $4 \times 4$ square grid (each square can only hold 1 coin). Find the probability that any two of the 3 coins are not in the same row or column.
First, calculate the total number of ways $N$.
The first coin can be placed in 16 cells, which gives 16 ways; the second coin can be placed in the remaining 15 cells, which gives 15 ways; the third coin can be placed in the remaining 14 cells, which gives 14 ways. Therefore, the total number of ways is
$$
N=16 \times 15 \times 14=3360 \text {. }
$$

Next, calculate the number of ways $m$ that meet the problem's requirements.
Since the first coin can be placed in 16 cells, which gives 16 ways, and there are 9 cells that are not in the same row or column as it, the second coin, which is not in the same row or column as the first coin, has 9 ways to be placed. There are 4 cells that are not in the same row or column as the first two coins, so the third coin can be placed in the remaining 4 cells, which gives 4 ways.
Therefore, the number of ways that meet the problem's requirements is
$$
m=16 \times 9 \times 4=576 \text {. }
$$

Thus, the required probability is $P=\frac{m}{N}=\frac{6}{35}$.
(Provided by the Sichuan Mathematical Competition Committee)