CA Foundation · Quantitative Aptitude · Permutations and Combinations
A surveyor marks 10 points on a plot map, of which exactly 4 lie on one straight line and no other three are collinear. How many triangles can be formed with these points as vertices?
The answer is 116 triangles. Choosing any three of the ten points gives 120 selections, but the 4 selections made entirely from the four collinear points lie on a line and give no triangle. Subtracting C(4,3) = 4 from 120 leaves 116.
- A120
- B116Correct
- C119
- D112
Explanation
Any 3 of the 10 points give C(10,3) = 120 selections. Selections of 3 points from the 4 collinear ones, C(4,3) = 4, do not form triangles. So triangles = 120 - 4 = 116. Subtracting only 1 (119) wrongly treats the collinear points as a single failed selection.
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