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How many triangles can be formed by choosing vertices of an octagon, such that none of the triangle’s sides coincides with any side of the octagon?
- 24
- 52
- 48
- 16
Correct answer: 16
Solution
Total triangles = C(8,3) = 56. Subtract those sharing exactly one side: 8 sides x 4 valid third vertices = 32. Subtract those sharing two sides (corner triangles) = 8. Remaining = 56 - 32 - 8 = 16.
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