Question

If three squares are chosen in a chess board, the chance that they should be in a diagonal line is.

• A. $\frac{7}{144}$
• B. $\frac{5}{744}$
• C. $\frac{7}{544}$
• D. $\frac{5}{372}$

Answer 1

Answer: (D)

$\frac{5}{372}$

Total squares $=64$
Ways of choosing 3 squares${=}^{64}{C}_3$
Squares on diagonals $=16$
Ways of choosing square from diagonal ${=}^{16}{C}_3$
P(sq. on diagonal) $=\frac{{}^{16}{C}_3}{{}^{64}{C}_3}$
$=\frac{\frac{16!}{13!3!}}{\frac{64!}{61!3!}}$
$=\frac{5}{12\times 31}$
$P=\frac{5}{372}$