A square of \( n \) units by \( n \) units is divided into \( n^{2} \) squares each of area 1 sq...

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A square of \( n \) units by \( n \) units is divided into \( n^{2} \) squares each of area 1 sq unit. Find the number of ways in which 4 points (out of \( (n+1)^{2} \) vertices of the squares) can be chosen so that they form the vertices of a square.
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