# GRE Permutation and geometry question

1. if you join all the vertices of a heptagon, how many quadrilaterals will you get?
2. How many heptagons can be drawn by joining the vertices of a polygon with 10 sides?
3. A polygon has 20 diagonals,how many sides does it have ? Are there are formula showing relation between diagonal and no of sides of a polygon?

These two questions are similar. Any clues to help me solve the problem.

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For 3., have you tried drawing different polygons and counting up the number of diagonals and looking for a pattern? –  Gerry Myerson Sep 11 '12 at 7:17

@sonam: Try reading this article. User33263 is suggesting (correctly) that you want $\binom74$ and $\binom{10}7$. –  Brian M. Scott Sep 11 '12 at 8:30