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The number of diagonals can be drawn in a hexagon is ______

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The number of diagonals can be drawn in a hexagon is ______

(a) 9

(b) 32

(c) 16

(d) 21

I have been asked this question in an online interview.

My question is taken from Counting in portion Counting of Discrete Mathematics

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The correct option is (a) 9

Easiest explanation: A hexagon has 6 sides. We obtain the diagonals by joining the vertices in pairs.

Total number of sides and diagonals = ^6C2 = \(\frac{6 * 5}{2 * 1}\) = 5×3 = 15. This includes its 6 sides also. So, Diagonals = 15 – 6 = 9. Hence, the number of diagonals is 9.

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