Find the number of triangles formed by joining 12 points if four points are collinear. - Mathematics and Statistics

Sum

Find the number of triangles formed by joining 12 points if four points are collinear.

Solution

There are 12 points 1n a plane of which four points are collinear.
If no three points are collinear, we will get 1003 triangles. Since four points are collinear, the number of triangles will reduce by 403.
∴ The number of triangles formed

= ""^12"C"_3 - ""^4"C"_3

= 220 - (4 xx 3 xx 2)/(3 xx 2)

= 220 – 4
= 216

Concept: Properties of Combinations
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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. (ii) | Page 90