COMEDK · Maths · 36. Probability
18 Points are indicated on the perimeter of a triangle \(\mathrm{ABC}\) as shown below. If three points are chosen then probability that it will from a triangle is
- A \(\dfrac{1}{2}\)
- B \(\dfrac{711}{816}\)
- C \(\dfrac{355}{408}\)
- D \(\dfrac{331}{816}\)
Answer & Solution
Correct Answer
(B) \(\dfrac{711}{816}\)
Step-by-step Solution
Detailed explanation
Total points on perimeter \(= 18\), with 7 points on each side (including vertices). Total ways to choose 3 points \(= \binom{18}{3} = \dfrac{18 \times 17 \times 16}{6} = 816\) 3 points are collinear (don't form a triangle) only when all 3 lie on the same side. Collinear sets…
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