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Question

ABCD is a convex quadrilateral. 3,4,5 and 6 points are marked on the sides AB,BC,CD and DA respectively. The no. of triangles with vertices on different sides are?


A

270

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B

220

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C

282

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D

342

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Solution

The correct option is D

342


Explanation for the correct option:

Find the number of triangles:

Given that there are 3 points on AB, 4 on BC, 5 on CD, 6 on DA

There are 4 possibilities to find the triangles whose vertices lie on different sides;

  1. AB,BC,CD:(3,4,5)C13xC14xC15=60
  2. BC,CD,DA:(4,5,6)C14xC15xC16=120
  3. CD,DA,AB:(5,6,3)C15xC16xC13=90
  4. DA,AB,BC:(6,3,4)C16xC13xC14=72

Total number of triangles =60+120+90+72

=342

Hence, option ‘D’ is correct.


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