Quantitative Aptitude Ques 1119

Question: The total number of triangles that can be formed from 12 points out of which 4 points arc collinear, is

Options:

A) 220

B) 224

C) 216

D) 210

Show Answer

Answer:

Correct Answer: C

Solution:

  • Total number of triangles which can be formed by selecting any three points from 12 points $ ={}^{12}C _3 $ Since, 4 points are collinear. Selecting three points from these 4 points $ ={}^{4}C _3 $ So, required number of triangles which can be formed $ ={}^{12}C _3-{}^{4}C _3 $ $ =\frac{12\times 11\times 10}{3\times 2\times 1}-\frac{4\times 3\times 2}{3\times 2\times 1} $ $ =220-4=216 $
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