if you 99 lines on a piece of paper so that no two lines are pallarel to each other and no three lines pass through the same point,how many times will they will intersect?

n lines can intersect in n(n-1)/2 points

Points of intersection 1

To find the number of intersections, we can use a formula known as the handshake formula. The formula states that the number of intersections can be calculated using the formula:

I = (N(N-1))/2

Where I is the number of intersections and N is the number of lines.

In this case, N = 99, as there are 99 lines on the piece of paper. Plugging in the values, we get:

I = (99(99-1))/2
I = (99(98))/2
I = 4851

So, there will be 4851 intersections among the 99 lines on the piece of paper.

To determine the number of times the lines will intersect, we can use a combinatorial approach.

First, let's consider the number of intersections that occur between any two lines. For every pair of lines, they will intersect at most once. This means that the total number of intersections between any two lines is given by the formula: nC2, where n is the number of lines.

In this case, we have 99 lines. Therefore, the number of intersections between any two lines is 99C2.

The formula for nC2 (n choose 2) is given by: nC2 = n! / (2! * (n-2)!)

Using this formula, we can calculate the value for 99C2:

99C2 = 99! / (2! * (99-2)!)
= 99! / (2! * 97!)
= (99 * 98) / 2

Simplifying further, we get:

99C2 = 99 * 98 / 2
= 99 * 49
= 4851

Therefore, the 99 lines will intersect a total of 4851 times.