No. of quadrilaterals in a polygon

[zorro]

Homework Statement

Quadrilaterals are formed by using the vertices of a convex polygon of 24 sides. The number of quadrilaterals having atleast one side of the quadrilateral in common with the side of the polygon is ?

The Attempt at a Solution

We can find out the total no. of quadrilaterals that can be formed and subtract from it the no. of quadrilaterals with no side common to that of the polygon.

²⁴C₄ - ¹²C₄ = 10131

I got 12 by choosing alternate vertices.
I don't get the correct answer this way :|

 

[coolul007]

I'm guessing here but what about 22C2 per side. You use 2 vertices for one side then you need 2 more to form the rest of the quadrilateral.