AP EAMCET · Maths · Permutation Combination
If four points are taken on each of three parallel lines in a plane, then the maximum number of triangles formed with these points is
- A 64
- B 144
- C 208
- D 80
Answer & Solution
Correct Answer
(C) 208
Step-by-step Solution
Detailed explanation
\(\text{Total triangles} = \binom{12}{3} - 3 \times \binom{4}{3}\) \(\binom{12}{3} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220\) \(\binom{4}{3} = 4\) \(\text{Total triangles} = 220 - 3 \times 4 = 220 - 12 = 208\)
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