There is a polygon of 10 sides. How many triangles can be drawn using the vertices of the polygon?

Correct option is A

Given:
Number of sides of the polygon = 10
Number of vertices of the polygon = 10
Formula Used:
Number of triangles that can be formed using n vertices is given by Combinations formula:
​$$^{n}C_{3} = \frac{n!}{3! × (n-3)!} = \frac{n × (n-1) × (n-2)}{3 × 2 × 1}$$​​
Solution:
A triangle is formed by joining any 3 non-collinear vertices.
Since all vertices of a polygon are points on its circumference (if cyclic) or lie in a way that no three consecutive vertices are collinear, we choose any 3 vertices out of the available 10 vertices.
Here, n = 10.
Number of triangles = $$^{10}C_{3}$$​​
Number of triangles = $$\frac{10 × 9 × 8}{3 × 2 × 1}$$​​
Number of triangles = 120
Final Answer
So the correct answer is (a)