Question

In how many ways is it possible to choose a white square and a black square on a chess board so that the squares must not lie in the same row or column -

• A. $56$
• B. $896$
• C. $60$
• D. $768$

Answer 1

The correct option is D $768$

We know a chess board has $32$ white and $32$ black squares, we need to select $1$ white square out of these $32$ white squares that is done in ${}^{32}{C}_1$ which is $32$

No, we have selected any one white square, there are eight black squares lying in the same column or row so out of $32-8=24$ black squares

We need to select one black square that is ${}^{24}{C}_1$

So, if both squares selected then our work is done

Hence it is in $32\times 24=768$ ways.