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  • There are n points in a plane, no three of which are collinear. If the number of triangles formed and the number of straight lines formed with these points are equal then n equals </

There are n points in a plane, no three of which are collinear. If the number of triangles formed and the number of straight lines formed with these points are equal then n equals 

Option: 1

4


Option: 2

5


Option: 3

6


Option: 4

9


Answers (1)

best_answer

As we have learned

There are n points in a plane such that no three of them are in the same straight line then the number of lines that can be formed by joining is/are ^{n}C_{2} and number of triangle is/are ^{n}C_{3}.

 

Now,

Number of triangles =  ^n C_ 3

Number of lines = ^n C_ 2

\therefore ^n C _3 = ^n C_ 2

   \\\Rightarrow ^n C _3 = ^n C_ {n-2} \Rightarrow n-2 = 3 \\ n = 5

 

 

 

 

Posted by

Rishabh

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