Question

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?

Answer 1

>> Answer

_________

`\:`

4rows, and 4columns.

Soo :

= 4!

= 4 × (4 - 1) × (4 - 2) × (4 - 3)

= 4 × 3 × 2 × 1

= 24

Answer 2

• 24 ways

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:

• 4*3*2*1 = 24