Number of Different Heptagons ($7$-sided polygons) which can be formed by joining the vertices of a polygon having $n$ sides, If none of the side of the polygon is the side of heptagon, is
My Try:
- Let us take $n$ sided regular polygon has vertices as $A_{1},A_{2},A_{3},\dotsc,A_{n-1},A_{n}$
- Now here we have to form a Heptagon none of whose side are the side of $\bf{Polygon}$
- Now If we take $A_{1}$ as one vertices, then we can not take $A_{2}$ and $A_{n}$ So here we have to take
- $6$ vertices from $n-3$ vertices such that no two vertices are consecutive.
- So the total number of ways equals $n$ times the number of ways in which no two vertices are consecutive.
So I did not understand how I can calculate that part, please help me.
Thanks.