Question

The $9$ horizontal and $9$ vertical lines on an $8\times 8$ chessboard from 'r' rectangles and 's' squares. The ratio $\frac{s}{r}$ in its lowest term,is

• A. $\frac{1}{6}$
• B. $\frac{17}{108}$
• C. $\frac{4}{27}$
• D. $\frac{6}{125}$

Answer 1

Answer: (B)

$\frac{17}{108}$

No. of rectangles $={}^9{C}_2{\times }^9{C}_2=1296$

No. of squares $=1^2+2^2+3^3+4^4+.........8^2=204$

$\therefore$ Required probability $=\frac{204}{1296}=\frac{17}{108}$