Question 58

There is a polygon of 11 sides. How many triangles can be drawn by only using the vertices of the polygon?

Solution

Given,

Number of sides of the polygon = 11

$$=$$> Number of vertices of the polygon = 11

Number of vertices of the triangle = 3

Number of possibilities of selecting 3 from 11 = $$11_{C_3}$$ =$$\frac{11\times10\times9}{1\times2\times3}$$ = $$165$$

$$\therefore\ $$Number of triangles that can be drawn by only using the vertices of the polygon of 11 sides = 165

Hence, the correct answer is Option C

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