Suppose that 20 pillars of the same height have been erected

Question:

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 beams is:

  1. 210

  2. 190

  3. 170

  4. 180


Correct Option: , 3

Solution:

Total cases $=$ number of diagonals

$={ }^{20} C_{2}-20=170$

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