Question

The number of ways in which we can place 3 white pawns and 3 black pawns on a 3 3 chessboard is equal to ________.

Answer 1

Answer:

The number of ways in which we can place 3 white pawns and 3 black pawns on a 3 3 chessboard is equal to 1680 ways

Step-by-step explanation:

For placing 3 white pawns and 3 black pawns firstly we need to select

6 positions ( 3 + 3 ) from 9 position

This can be done in ⁹C ₆ways = 84 ways

Now these 6 pawns will arrange themselves in 6! / ( 3! * 3! ) ways

 [ ( 3! * 3! ) because there are 3 white and 3 black pawns ]

= 720 / ( 6 * 6 )

= 20 ways

So,

Total number of ways = ⁹C ₆ * ( 6! / ( 3! * 3! ) )

=  84 * 20

= 1680 ways

Hence,

The number of ways in which we can place 3 white pawns and 3 black pawns on a 3 3 chessboard is equal to 1680 ways