Problem: 15 points are taken on the circumference of a circle, and through any two of them a chord is drawn. Suppose that no three chords intersect at the same point inside the circle. How many points of intersections are between these chords?
I know that you need atleast 4 distinct points on the circumference to have an intersection. If i can show that a bijection is true for n points then I can easily say how many points of intersections occur for fifteen points. I know to prove a bijection I must also prove that it is injective and surjective however I get stuck when creating the function.
if(fx) = f(y) then f=y
so I have a function
k(x) = x(1/4). where x >= 4.
However my function fails when I input 5 since you cant have 1.25 intersections. any help?