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(C) The $20$ pillars form the vertices of a $20$-sided polygon.Connecting the top of each pillar to all non-adjacent pillars is equivalent to finding

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$170$

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(C) The $20$ pillars form the vertices of a $20$-sided polygon.Connecting the top of each pillar to all non-adjacent pillars is equivalent to finding the number of diagonals in a $20$-sided polygon.The total number of ways to choose $2$ pillars out of $20$ is given by $^{20}C_2$.$^{20}C_2 = \frac{20 	imes 19}{2} = 190$.These $190$ connections include the $20$ sides of the polygon (which connect adjacent pillars).Therefore,the number of beams (diagonals) is $190 - 20 = 170$.

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is

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