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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2011 · Mathematics · Permutation and Combination

A, B, C, D and E are coplanar points and three of them lie in a...

A,B,C,DA, B, C, D and EE are coplanar points and three of them lie in a straight line. What is the maximum number of triangles that can be drawn with these points as their vertices?

Options

  1. A5
  2. B9
  3. C10
  4. D12

Correct answer

B. 9

Step-by-step solution

Total number of points =5=5 Now a triangle has three vertices ∴\therefore Number of triangles forms =5c3=5 c_3 But it is given that three points are collinear. So that maximum number of triangles formed =5c3−3c3=5×42−1=10−1=9=5 c_3-3 c_3=\frac{5 \times 4}{2}-1=10-1=9
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