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Combination

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Question

The vertices of a regular polygon of 12 sides are joined to form triangles. The number of triangles which do not have their sides as the sides of the polygon is

A

96

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B

108

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C

11

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D

220

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Solution

The correct option is C
11

$T o t a l N o . o f Δ l e s = 12_{C 3} = 220$

$N o . o f Δ l e s w i t h t w o s i d e s c o m m o n w i t h p o l y g o n = 12$

$N o . o f Δ l e s w i t h a l l s i d e c o m m o n = 8.12 = 96$

$∴ a n s = 220 - (12 + 96) = 112$

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