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in Permutations and Combinations by (48.0k points)

Find the number of diagonals of a decagon.

1 Answer

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Best answer

There are 10 vertices in a decagon. 

Now by joining two vertices, we get a side of decagon or a diagonal.

Hence, the number of the line segment by joining of vertices of decagon = number of ways taking 2 points out of 10 points

= 10C2 = (10(10 - ))/2!

Now, there are 10 sides of decagon in 10C2 line segment

∴ Required number of diagonals

Hence, the number of diagonals is 35.

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