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27 Aug 2008, 08:33
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How many diagonals does a polygon with 21 sides have, if one of its vertices does not connect to any diagonal?
a) 21
b) 170
c) 340
d) 357
e) 420
a) 21
b) 170
c) 340
d) 357
e) 420
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27 Aug 2008, 09:18
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Nihit
I think 170...
take any point. You have 20 other points. Of these 20, 2 will be adjacent and so no diagonal with them. 18 possibilities. But one point has no diagonal with any other point. So for the chosen point, there are 17 diagonals possible.
This applies to 20 points (excluding the one that does not have diagonal with any point)
So you have 17*20. This includes double counting. So divide by 2
170.
I am interested in knowing how combination can be used to tackle this problem.
27 Aug 2008, 09:33
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bhushangiri
Let say polygon has n points.
chose any 2 points to make line.
= nC2 combinations (include all sides and all diagnols)
= n(n-1)/2
no of diagnols = n(n-1)/2 - n = n(n-3)/2
Here one vertex is not participating..
visualize that it is 20 sides polygon..
= 20*17/2 - 1 (side is actually not present ) +1 ( actually that side is diagnol)
=170
