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How many triangles can be formed by joining the vertices of a pentagon?
- A10
- B20
- C30
- D40
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CCommunity
Let the vertices of the pentagon be A1, A2, A3, A4 and A5.
One triangle is formed by selecting a group of 3 points from the 5 given vertices.
⇒ Number of triangles = Number of groups of 3 each from 5 points
⇒ 5C3 = 5!/{(5 - 3)! × 3!} = 10
∴ The number of triangles that can be formed by joining the vertices of a pentagon = 10
One triangle is formed by selecting a group of 3 points from the 5 given vertices.
⇒ Number of triangles = Number of groups of 3 each from 5 points
⇒ 5C3 = 5!/{(5 - 3)! × 3!} = 10
∴ The number of triangles that can be formed by joining the vertices of a pentagon = 10