Two squares chosen at random on a chessboard.

Question

Two squares chosen at random on a chessboard. Find the probability they share a side.

Accepted Answer

Total ways $={}^{64}C_2$. Adjacent pairs: $2\times7\times8=112$ (horizontal + vertical adjacencies).

$$P = \frac{112}{{}^{64}C_2} = \frac{112}{2016}=\frac{1}{18}$$

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