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प्रश्न
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8
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उत्तर
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 = 8 sides
∴ the number of diagonals that can be drawn
= 8C2 – 8
= `(8!)/(2!6!) - 8`
= `(8 xx 7 xx 6!)/(2 xx 6!) - 8`
= 28 – 8
= 20
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