Question

the maximum number of points of intersection of 8 straight lines is

Answer 1

In the above question, we have to find the maximum number of points of intersection for 8 straight lines .

Solution -

We have been given 8 straight lines .

Now ,

We get a point of intersection only when two straight lines intersect .

For two lines to intersect , we have the following condition -

These two lines must not be parallel .

Refer to the above attached figure .

Now, when we take the case of 8 straight lines , the scenario becomes a bit different .

To maximize the points of Intersection , we have the following condition -

None of these lines must pass through the intersection point of any other lines .

So ,

We can write this as -

8 C 2

=> 8 ! / [ ( 8 - 2 ) ! × 2 ! ]

=> 8! / [ 6 ! × 2 ]

=> { 8 × 7 × 6 ! } / { 6 ! × 2 }

=> 56 / 2

=> 28 .

Thus , the maximum number of intersection point of 8 straight lines is 28 .

This is the required answer .

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