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

Options

A. 180
B. 210
C. 170
D. 190

Answer

C

Explanation

It is given that, there are 20 pillars of the same height have been erected along the boundary of a circular stadium.
Now, the top of each pillar has been connected by beams with the top of all its non - adjacent pillars, then total number of beams = number of diagonals of 20 - sided polygon.
`because ""^(20)C_(2)` is selection of any two vertices of 20 - sided polygon which included the sides as well.
So, required number of total beams `= ""^(20)C_(2) - 20`
[`because` the number of diagonals in a n - sided closed polygon `= ""^(n)C_(2) - n`]
`= (20 XX 19)/(2) - 20`
= 190 - 20 = 170