12 identical coins are placed in the cells on a chess board with 4 rows and 4 columns. If coins are not allowed to be placed in the same cell, how many ways are there so that there are 3 coins in every rows
and columns?

Step-by-step explanation:

If the coins are identical and not numbered, we need to find the number of patterns.

There are 4 rows and 4 columns. One cell remains empty in each row.

There are 4 options for the first row, 3 options for the second row, 2 options for the third row and 1 option for the fourth row.

The number of options reduces to avoid more than 1 empty cell in each row or column.

Number of options is:

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.