CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

The question is from Permutation and Combination. This question is about Forming Triangles. Our task is to find out the number of triangles that can be formed from some points. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 28: Of 22 points on a plane, 8 are on a straight line, 7 are on another straight line and 10 are on a third straight line. How many triangles can be drawn by connecting some three points from these 22?

1. ²²C₃
2. ²²C₃ - (⁸C₃+ ⁷C₃ +¹⁰C₃)
3. ²²C₃ + (⁸C₃+ ⁷C₃ +¹⁰C₃)
4. ⁸C₃+ ⁷C₃ +¹⁰C₃

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: Clue - FInd the number of rearrangements and then focus on the number of digits

From the 22 points on a plane we can form ²²C₃ triangles but it is given that 8 are on one straight line, 7 are on another straight line and 10 more are on another straight line, so we can form triangles on joining points which are on straight lines
so we have to subtract (⁸C₃+ ⁷C₃ +¹⁰C₃) from the total.
Hence, we can form ²²C₃ - (⁸C₃+ ⁷C₃ +¹⁰C₃) triangles.

The question is "How many triangles can be drawn by connecting some three points from these 22?"

Hence the answer is "²²C₃ - (⁸C₃+ ⁷C₃ +¹⁰C₃)"

Choice B is the correct answer.