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

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

JEE MainJEE Main 2021Permutations and Combinations

Solution:

Total ways of choosing square $={ }^{64} C _{2}$
$=\frac{64 \times 63}{2 \times 1}=32 \times 63$
ways of choosing two squares having common side
$=2(7 \times 8)=112$
Required probability $=\frac{112}{32 \times 63}=\frac{16}{32 \times 9}=\frac{1}{18}$