Two squares are chosen

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is.

  1. $\frac{2}{7}$

  2. $\frac{1}{18}$

  3. $\frac{1}{7}$

  4. $\frac{1}{9}$

Correct Option: , 2


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 $=\frac{112}{32 \times 63}=\frac{16}{32 \times 9}=\frac{1}{18}$


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