**Q. A painter draws 64 equal squares of 1 square inch on a square canvas measuring 64 square inches. She chooses two squares (1 square inch each) randomly and then paints them. What is the probability that two painted squares have a common side?**

## EXPLANATION

Since there are 64 squares on 1 cm^{2} each on a canvas of 64 cm^{2} area, The squares should form a lattice just the Chessboard.

The two adjacent squares can be adjacent in the same row or the same column.

In the same row, there can be 7 sets of adjacent pairs of squares.

Since there are 8 rows, It can be done in 8×7 ways.

Similarly, there will be 8×7 ways of painting vertically adjacent squares.

So, totally there will be 2×8×7=122 ways of adjacent pairs of squares.

From the 64 squares, 2 squares can be selected in ^{64}C_{2}

= 64 x 63 / 2 x 1 = 2016 ways

The probability of finding two adjacent squares = 112/2016

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