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  • A circle has 14 points on it. What is the highest number of distinct lines can be made, each of which passes through two of these points?   <div class='qna-option'

A circle has 14 points on it. What is the highest number of distinct lines can be made, each of which passes through two of these points? 

 

Option: 1

430


Option: 2

330


Option: 3

490


Option: 4

390

 


Answers (1)

best_answer

Given that,

There are 14 points on a circle.

We can draw a line with two points on a circle that has 14 points.

If we choose two distinct points from those 14, we will obtain a line.

As a result, the number of various lines equals the number of ways to choose two points out of 14 points.

Thus,

\mathrm{\begin{aligned} &{ }^{14} C_2=\frac{14 !}{2 ! 12 !}\\ &{ }^{14} C_2=\frac{14 \times 13}{2}\\ &{ }^{14} C_2=91 \end{aligned}}

Therefore, the number of different lines that can be drawn so that each line passes through two of these points is 91.

Posted by

avinash.dongre

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