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Question: The number of diagonals of a polygon of m sides is –...

The number of diagonals of a polygon of m sides is –

A

m(m−1)2!\frac{m(m - 1)}{2!}

B

m(m−2)2!\frac{m(m - 2)}{2!}

C

m(m−3)2!\frac{m(m - 3)}{2!}

D

m(m−5)2!\frac{m(m - 5)}{2!}

Answer

m(m−3)2!\frac{m(m - 3)}{2!}

Explanation

Solution

No. of sides = m, no. of vertices = m

No. of lines = mC2, No. of diagonals = mC2 – m

= m(m−1)2\frac{m(m - 1)}{2} – m = m(m−3)2\frac{m(m - 3)}{2}