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Combination Based on Geometry

There are 12 ...

Question

There are 12 points in a plane of which 5 are in a line. Then the number of distinct quadrilaterals with vertices at these points is

A

35

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B

175

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C

210

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D

420

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Solution

The correct option is D 420
Number of quadrilaterals $=^{7} C_{4} +^{5} C_{1}^{7} C_{3} +^{5} C_{2}^{7} C_{2}$ $= 35 + 5 \times 35 + 10 \times 21$ $= 210 + 210 = 420$

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