Below is a standard chessboard1 In the following problems pi

Below is a standard chessboard.1 In the following problems, pieces of the same type are considered interchangeable (i.e. all white pawns are the same, all black rooks are the same, etc) but not across color (a white pawn is different from a black pawn).

(a) How many ways are there to place the white king on a white square? (b) How many ways are there to set up the pieces in the back ranks of both white and black i.e. arrange the two rooks, two knights, two bishops, king and queen on the first row of 8 squares.2 (c) How many ways are there to arrange the pieces on the board?

Solution

a)

There are total 64 in the chess board and 32 white

Number ways are there to place the white king on a white square is 32C1 =32

C)

There are total 32 pieces on the board

Hence total number of ways are there to arrange the pieces on the board=64c₃₂