CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
Ten points lie in a plane, of which exactly 4 are collinear and no other three are collinear. How many distinct triangles can be formed by joining these points?
116 triangles can be formed. Any three of the 10 points give 10C3 = 120 triples, but the 4C3 = 4 triples chosen from the four collinear points do not form triangles. Subtracting gives 120 minus 4, which equals 116.
- A120
- B116Correct
- C124
- D84
Explanation
Total triples = 10C3 = 120. Three points from the 4 collinear ones form no triangle: 4C3 = 4. Triangles = 120-4 = 116. Option 120 ignores the collinear points.
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