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  • In a plane with 8 points, 4 of them are the only ones that can be connected in a straight line by three points. Determine how many triangles can be created by joining them in an equal pos

In a plane with 8 points, 4 of them are the only ones that can be connected in a straight line by three points. Determine how many triangles can be created by joining them in an equal position.

 

Option: 1

42


Option: 2

52


Option: 3

60


Option: 4

74


Answers (1)

best_answer

Given that,

There are 8 points in a plane.

The number of 8 points in a plane is given by,

\mathrm{\begin{aligned} &{ }^8 C_3=\frac{8 !}{3 ! 5 !}\\ &{ }^8 C_3=\frac{8 \times 7 \times 6}{3 \times 2}\\ &{ }^8 C_3=56\\ \end{aligned}}

Points 4 of them are the only ones that can be connected in a straight line by three points given by,

\mathrm{{ }^4 C_3=\frac{4 !}{3 !}\\ }

\mathrm{{ }^4 C_3=4}

Therefore, the total number of triangles formed is 56 - 4 = 52.

 

Posted by

Irshad Anwar

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