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Six points are there on a circle from wh...

Six points are there on a circle from which two triangles drawn with no vertex common. Find the probability that none of the sides of the triangles intersect.

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To solve the problem of finding the probability that none of the sides of two triangles drawn from six points on a circle intersect, we can follow these steps: ### Step 1: Determine the Total Number of Ways to Choose Two Triangles We need to select two triangles from the six points on the circle, ensuring that the triangles do not share any vertices. 1. **Choose 3 points for the first triangle**: This can be done in \( \binom{6}{3} \) ways. 2. **Choose 3 points for the second triangle**: After choosing the first triangle, there are no points left for the second triangle since they cannot share vertices. Therefore, the second triangle must also be formed from the remaining points. ...
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