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

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14.Probability

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

A

$\frac{2}{7}$

B

$\frac{1}{18}$

C

$\frac{1}{7}$

D

$\frac{1}{9}$

(JEE MAIN-2021)

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

Standard 11

Mathematics

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