- #1

member 428835

- Homework Statement
- How many quadrilaterals can be formed from n-polygon (convex) given no adjacent sides of the polygon are used?

- Relevant Equations
- Nothing comes to mind.

My thought it to think of the orientation as a string: let V denote a selected vertex and E denote a vertex that's not selected. There are then 4 V's to distribute and ##n-4## E's to distribute. Then just choosing quadrilaterals without restriction we have ##n!/(4!(n-4)!)##. However, we want no adjacent sides. I'm thinking instead of selecting V,V,V,V we now position VE,VE,VE,VE with the remaining ##n-8## E's going anywhere without restriction. Thus the number of quadrilaters without adjacent sides is ##(n-8+4)!/((n-8)!4!)##. Is this correct, or am I missing something?