Permutation-Combination
Aptitude

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Q.

There are $7$ non-collinear points. How many triangles can be drawn by joining these points?

 A.

$35$

 B.

$10$

 C.

$8$

 D.

$7$

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Solution:
Option(A) is correct

A triangle is formed by joining any three non-collinear points in pairs.

There are $7$ non-collinear points.

The number of triangles formed,

$= {^7C_3}$

$= \dfrac{7 × (7-1) × (7-2)}{3!}$

$= \dfrac{7 × 6 × 5}{3 × 2 × 1}$

$= 7 × 5$

$= 35$


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