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 lies in the same row or column?

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

Answer 1

The correct option is D $768$

A white square can be selected in $32$ ways.
There will be $32$ black squares on the board. Of these $4$ black squares will be in the row in which the selected white square lies.
Also, $4$ black squares will be in the column in which the selected white square lies.
So if we do not take theses $8$, we have $24$ squares to choose from, therefore number of outcomes $=$ $32\times 24$ =$768$.