Question:
Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is.
Correct Option: , 2
Solution:
Total ways of choosing square $={ }^{64} \mathrm{C}_{2}$
$=\frac{64 \times 63}{2 \times 1}=32 \times 63$
ways of choosing two squares having common side $=2(7 \times 8)=112$
Required probability $=\frac{112}{32 \times 63}=\frac{16}{32 \times 9}=\frac{1}{18}$