Two squares are chosen at random on a chessbo | vedclass

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(B) Total number of ways to choose $2$ squares from $64$ is given by ${}^{64}C_{2}$.${}^{64}C_{2} = \frac{64 	imes 63}{2} = 32 	imes 63 = 2016$.To f

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$\frac{1}{18}$

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(B) Total number of ways to choose $2$ squares from $64$ is given by ${}^{64}C_{2}$.${}^{64}C_{2} = \frac{64 	imes 63}{2} = 32 	imes 63 = 2016$.To find the number of pairs of squares with a common side,we count the horizontal and vertical adjacent pairs.In each row of $8$ squares,there are $7$ pairs of adjacent squares. Since there are $8$ rows,there are $8 	imes 7 = 56$ horizontal pairs.Similarly,in each column of $8$ squares,there are $7$ pairs of adjacent squares. Since there are $8$ columns,there are $8 	imes 7 = 56$ vertical pairs.Total number of favorable pairs $= 56 + 56 = 112$.The probability is $\frac{112}{2016} = \frac{112}{32 	imes 63} = \frac{16}{32 	imes 9} = \frac{1}{2 	imes 9} = \frac{1}{18}$.

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

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