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The number of diagonals can be drawn in a hexagon is ______(a) 9(b) 32(c) 16(d) 21I have been asked this question in an online interview.My question is taken from Counting in portion Counting of Discrete Mathematics

Answer»

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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