Question

if you draw 35 lines on a piece of paper so that no two lines are parallel to each other and no three lines are concurrent, how many times will they intersect?

Answer 1

Answer:

The lines will intersect 595 times.

Step-by-step explanation:

We can do it in 2 methods.

1st method:- Let us count the number of intersections by drawing lines one by one.

1st line - 0 points=0

2nd line- new 1 point=1

3rd line - old 1 point + new 2 points with two old lines = 1+2

4th line - old (1+2) points+ new 3 points= 1+2+3

5th line - old (1+2+3) points + new 4 points=1+2+3+4

Like that from 35th line-1+2+3+4......34 = $\frac{34X35}{2}=595$

2nd method:-

We have to choose 2 lines from 35 lines.

We can do it in $35_{C} _{2}$ ways = 595 points