# 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
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## 1 Answer

1. You need to choose 4 vertices from 7 vertices of Heptagon. How do you do that?
2. Same as 1, you need to select 7 out of 10.
3. No of distance diagonals is n(n-3)/2; you can do this if you can get above 2.
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thanks for number 3 but i could not figure out 1 and 2, –  sonam Sep 11 '12 at 7:57
Its simple combination problem, you need to select 4 out of 7, it 7C4. {as the order doesn't matter} –  Ram Sep 11 '12 at 8:21
@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
But there will be many quadrilaterals that won't have vertices on the Heptagon. –  Saurabh Sep 11 '12 at 8:33
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