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permutation and combination — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSpermutation and combination1 Mark
MCQ
Consider a rectangle $ABCD$ having $5,7,6,9$ points in the interior of the line segments $AB,CD , BC , DA$ respectively. Let $\alpha$ be the number of triangles having these points from different sides as vertices and $\beta$ be the number of quadrilaterals having these points from different sides as vertices. Then $(\beta-\alpha)$ is equal to :
  • A
    $795$
  • B
    $1173$
  • C
    $1890$
  • ✓
    $717$
✓

Answer

Correct option: D.
$717$
d
$\alpha=$ Number of triangles

$\alpha=5 \cdot 6 \cdot 7+5 \cdot 7 \cdot 9+5 \cdot 6 \cdot 9+6 \cdot 7 \cdot 9$

$\quad=210+315+270+378$

$\quad=1173$

$\beta=$ Number of Quadrilateral

$\beta=5 \cdot 6 \cdot 7 \cdot 9=1890$

$\beta-\alpha=1890-1173=717$

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