What is the number of points of intersection of the diagonals of a regular convex polygon (other than the vertices of the polygon) with 7 sides?

A. 27

B. 35

C. 31

D. 42

B. 35

As we know that no two diagonals are parallel in the polygon with odd number of sides.
If we take any 4 vertices then we get one intersection point.
So, we need to select 4 vertices out of 7 vertices.

$\mathrm{C}_{\mathrm{4}}^{\mathrm{7}}$ = 35