JEE MAIN - Mathematics (2021 - 1st September Evening Shift - No. 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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$${2 \over 7}$$
$${1 \over 18}$$
$${1 \over 7}$$
$${1 \over 9}$$
Explanation
Total ways of choosing square = $${}^{64}{C_2}$$
$$ = {{64 \times 63} \over {2 \times 1}} = 32 \times 63$$
ways of choosing two squares having common side = 2 (7 $$\times$$ 8) = 112
Required probability $$ = {{112} \over {32 \times 63}} = {{16} \over {32 \times 9}} = {1 \over {18}}$$.
Ans. (b)
$$ = {{64 \times 63} \over {2 \times 1}} = 32 \times 63$$
ways of choosing two squares having common side = 2 (7 $$\times$$ 8) = 112
Required probability $$ = {{112} \over {32 \times 63}} = {{16} \over {32 \times 9}} = {1 \over {18}}$$.
Ans. (b)
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