Question

the maximum number of intersection points when 100 straight lines are drawn on a piece of paper​

Answer 1

Explanation:

As we have n number of line, and we have to find maximum point of intersection using these n line. So this can be done using combination. This problem can be think as number of ways to select any two line among n line. As every line intersect with other that is selected.

Answer 2

The maximum number of intersection points of 100 straight lines is 4950

GIVEN

Number of straight lines.

TO Find

Number of intersection points.

SOLUTION

We can simply solve the problem as under -

If two straight lines are intersecting, the intersecting point will be 1

Conditions for lines to intersect-

1. For lines to intersect each other in a plane they should not be parallel to one another.
2. And no line should should pass through the similar points.

We can write this as-

$¹⁰⁰C₂ = 100! / [ (100-2)! × 2! ]$

$= { 100× 99×98! }/ {98! × 2 }$

=99 × 100 /2

= 495

The maximum number of intersection points of 100 straight lines is 4950

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