# Suppose that 20 pillars of the same height have been erected along the boundaryof a circular stadium. If the top of each pillar has been connected by beams with thetop of all its non-adjacent pillars, then the total number of beams is :  Option 1) 170 Option 2) 180 Option 3) 210 Option 4) 190

Any two non-adjacent pillars are joined by beams.

$\therefore$ no. of beams = no. of diagonals

$=^{20}C_2-20$

$=\frac{20\times 19}{2}-20$

$=190-20$

$=170$

Option (1) is correct.

Option 1)

170

Option 2)

180

Option 3)

210

Option 4)

190

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