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  • Consider a rectangle ABCD having 5,7,6,9 points in the interior of the line segements AB, CD, BC, DA respectively. Let  be the number of triangles having these points from different sides as ve

Consider a rectangle ABCD having 5,7,6,9 points in the interior of the line segements AB, CD, BC, DA respectively. Let \alpha be the number of triangles having these points from different sides as vertices and \beta be the number of quadrilaterals havings these points from different sides as vertices. Then (\beta - \alpha) is equal to:
Option: 1 1890
Option: 2 795
Option: 3 717
Option: 4 1173

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\begin{aligned} \alpha &=\text { Number of triangles } \\ \alpha &=5 \cdot 6 \cdot 7+5 \cdot 7 \cdot 9+5 \cdot 6 \cdot 9+6 \cdot 7 \cdot 9 \\ &=210+315+270+378 \\ &=1173 \\ \beta &=\text { Number of Quadrilateral } \\ \beta &=5 \cdot 6 \cdot 7 \cdot 9=1890 \\ \beta &-\alpha=1890-1173=717 \end{aligned}

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Suraj Bhandari

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