Tamil Nadu Board of Secondary EducationHSC Arts Class 11

How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points? - Mathematics

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Sum

How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?

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Solution

Number of points 15

To form a triangle we need 3 non-collinear points.

The number of ways of selecting 3 non-collinear points from 15 points is = 15C

= `(15!)/(3!(15 - 3)!)`

= `(15!)/(3!  2!)`

= `(15 xx 14 xx 13 xx 12!)/(3 xx 2!)`

= `(15 xx 14 xx 1)/(3 xx 2 xx 1)`

= 5 × 7 × 13

= 455

Concept: Combinations
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Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.3 [Page 187]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.3 | Q 22 | Page 187

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