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Question

Two small squares on a chess board are chosen at random. Probability that they have a common side is


A
13
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B
19
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C
118
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D
None of these
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Solution

The correct option is C $$\displaystyle \frac { 1 }{ 18 } $$
There are $$64$$ small squares on a chess board.

$$\Rightarrow$$ Total number of ways to choose two squares $$=_{  }^{ 64 }{ { C }_{ 2 } }=32\times 63$$
For favorable ways we must choose two consecutive small squares for any row or any column
$$\Rightarrow$$ number of favorable ways $$=(7\times 8)2$$
$$\Rightarrow $$ Required probability $$\displaystyle =\frac { 7\times 8\times 2 }{ 32\times 63 } =\frac { 1 }{ 18 } $$

Maths

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