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How many triangles can be formed by joining the vertices of a 10-sided polygon?

How many triangles can be formed by joining the vertices of a 10-sided polygon?-example-1

1 Answer

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The total number of triangles formed by joining vertices of 10-sided polygon is given by the combination of 10 sides taken at 3, i.e. selection of 3 points from 10 points ( because a triangle has 3 vertices). This gives


10C3=(10!)/(3!(10-3)!)=(10!)/(3!\cdot7!)=(10\cdot9\cdot8)/(6)=(720)/(6)=120

Then, the answer is the last option: 120

User Nawfal Serrar
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