# Find the number of triangles formed by joining 12 points if no three points are collinear, - Mathematics and Statistics

Sum

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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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.6 | Q 14. (i) | Page 90