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Question
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
Solution
There are n vertices in the polygon of n-sides.
If we join any two vertices, we get either side or the diagonal of the polygon.
Two vertices can be joined in nC2 ways.
∴ total number of sides and diagonals = nC2
But there are n sides in the polygon.
∴ total number of the diagonals = nC2 – n
n = 15 sides
∴ the number of diagonal that can be drawn
= 15C2 – 15
=`(15!)/(2!13!) - 15`
= `(15 xx 14 xx 13!)/(2 xx 13!) - 15`
= `(15 xx 14)/2 - 15`
= 105 – 15
= 90
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