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Question
Find the number of triangles formed by joining 12 points if no three points are collinear,
Solution
There are 12 points in a plane.
When no three of them are collinear.
We need three non-collinear points to form a triangle.
∴ The number of triangles formed 12C3
= `(12!)/((12 - 3)!3!)`
= `(12!)/((9!3!)`
= `(12xx11xx10xx9!)/(3xx2xx1xx9!)`
= 220
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