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  • Rows and columns on a chessboard are labeled A through H and 1-8. Meera has a bishop and a rook that he must put on the board so they are not in the same row or column. What is the total number of

Rows and columns on a chessboard are labeled A through H and 1-8. Meera has a bishop and a rook that he must put on the board so they are not in the same row or column. What is the total number of ways he can position the two pieces?

Option: 1

2136


Option: 2

1136


Option: 3

3136


Option: 4

4136


Answers (1)

best_answer

Given that,

The bishop and the rook have to be placed in a different row and column on a chessboard.

Let us choose one of the 64 boxes for placing the knight, with the number of ways equal to ^{61}C_{1}.

Row 6 and column A in a chessboard is no longer available for bishop placement. 

Thus, the remaining boxes are 64 - (8 + 7) = 49

The bishop can be placed in any of 49 boxes, with the number of ways equaling ^{49}C_{1}.

Hence, the total number of possible ways is given by, 

\mathrm{ { }^{49} C_1 \times{ }^{64} C_1=\frac{49 !}{48 !} \times \frac{64 !}{63 !} }

\mathrm{{ }^{49} C_1 \times{ }^{64} C_1=49 \times 64}

\mathrm{{ }^{49} C_1 \times{ }^{64} C_1=3136}

Therefore, the total number of ways is 3136 ways.

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