Question

If I have a $4 \times 4$ chess board, in how many ways can I place four distinct pawns on the board such that each column and row of the board contains no more than one pawn?

Answer 1

Answer:

576 ways

Step-by-step explanation:

There are 4 choices for the column of pawn in the 1st row

There are 3 choices for the column of pawn in the 2nd row,

There are 2 choices for the column of pawn in the 3rd row, and

There is 1 choice for the column of the pawn in the 4th row

Which gives a total of 4! = 24

Also, the pawns are distinct, so there are 4! ways to place them in these chosen positions;

4! = 24

So, there are 24 * 24 possible ways

= 576 ways