Find the number of polygons that can be formed, none of whose sides coincide with those of the n-sided polygon.
Since we have to form an r sided polygon, it is obvious that we would have to select r vertices from the n vertices of the n-sided polygon the restriction being, that no consecutive vertices should be chosen.
So to ensure that these vertices are separated we can select $n-r \choose r$ vertices that are between the selected vertices as separators.
This is where I got stuck. I tried searching the web but couldn't find any satisfactory explanations. Could someone please help me out with the logical approach to solve this?