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  • Find the maximum number of triangles that may be created using 8 points in a line and 4 points on a parallel line.  Option: 1 <

Find the maximum number of triangles that may be created using 8 points in a line and 4 points on a parallel line.

 

Option: 1

130


Option: 2

160


Option: 3

140


Option: 4

120


Answers (1)

best_answer

Given that,

The total points given is 12 points.

There are 8 points in a line and 4 points on a parallel line.

The number of edges for a triangle is 3.

Thus, the required number of ways is given by,

\mathrm[{ }^{12} C_3-{ }^8 C_3-{ }^4 C_3=\frac{12 !}{3 ! 9 !}-\frac{8 !}{3 ! 5 !}-\frac{4 !}{3 ! 1 !}]

\mathrm{{ }^{12} C_3-{ }^8 C_3-{ }^4 C_3=220-56-4}

\mathrm{{ }^{12} C_3-{ }^8 C_3-{ }^4 C_3=160}

Therefore, the total number of ways the triangle formed is 160 ways.

 

Posted by

Sanket Gandhi

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