Question

Number of ways of selecting three squares on a chessboard so that all the three be on a diagonal line of the board or parallel to it is

• A. $196$
• B. $126$
• C. $252$
• D. $392$

Answer 1

The correct option is D $392$

There are total $64$ squares in the chess board.

$8$ squares on the diagonal lines, $7$ squares on each consecutive side of diagonal line, $6$ on next to consecutive line of diagonal line and so on.

$\therefore$ Number of ways

$=\left[{(}^3{C}_3{+}^4{C}_3{+}^5{C}_3{+}^6{C}_3{+}^7{C}_3\right)\times 2{+}^8{C}_3]\times 2$
$=392$.

Hence, option D is correct.