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प्रश्न
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
उत्तर
Two points are needed to draw a segment.
A polygon of n sides has n vertices.
So, in a polygon of n sides, there will be
nC2 segments, which include its sides and diagonals both.
Since the polygon has n sides, the number of its diagonals is nC2 – n
Here, n = 15
∴ The number of diagonals = 15C2 – 15
= `(15!)/((15 - 2)!2!) - 15`
= `(15 xx 14)/2 - 15`
= 105 – 15
= 90
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