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Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct?

1. The number of straight lines that can be drawn by joining any two of these points is 380.

2. The number of triangles that can be drawn by joining any three of these points is 1140.

Select the correct answer using the code given below.

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  1. 1 only
  2. 2 only
  3. Both 1 and 2
  4. Neither 1 nor 2

Answer (Detailed Solution Below)

Option 2 : 2 only
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Detailed Solution

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Explanation:

We only need 2 points to form straight lines

We have 20 points so the number of straight lines drawn is 20C2 ​= 190
 

We only need 3 points to form a triangle

We have 20 points, so number of triangles drawn is 20C3 = 1140

∴ Statement 1 is incorrect and Statement 2 is correct.

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