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

Answer: (D)

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