Consider 37 points in a plane such that no three of them are collinear. A student is told to 1st draw all the possible polyg0ns of same number of sides & then draw all the possible diagonals. What is the maximum number of such diagonals possible? ( if a particular line is diagonal of two polygon then count both of them)

(Q). Consider 37 points in a plane such that no three of them are collinear. A student is told to 1st draw all the possible polyg0ns of same number of sides & then draw all the possible diagonals. What is the maximum number of such diagonals possible? ( if a particular line is diagonal of two polygon then count both of them)
Solution:-
we know that ³⁷Cᵣ will have maximum value when 
r =   = 18
          or
r =   = 19
and from one polygon we will get    = 135 diagonals.
Hence maximum number of diagonals is = 135.(³⁷C₁₈)        Answer