If two squares are chosen at random on a chess board, the probabi… - Vidyadip

MCQ

If two squares are chosen at random on a chess board, the probability that they have a side common is

A
$\frac{2}{7}$
B
$\frac{1}{18}$
C
$\frac{1}{9}$
D
$\frac{4}{9}$

✓

Answer

(b) $\frac{1}{18}$
Explanation: Total number of squares $=64$.
Two squares can be selected in ${ }^{64} C_2$ ways.
In each column, there are 7 pairs of adjacent squares where each pair share 1 side in common.
Total such pairs $=8 \times 7=56$.
In each row, there are 7 pairs of adjacent squares where each pair share 1 side in common.
Total such pairs $=8 \times 7=56$.
Therefore, favourable cases $=56+56=112$.
Required probability $=\frac{112}{{ }^{64} C_2}=\frac{112}{2018}=\frac{1}{18}$

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