Question

Suppose we have $10points$ in a plane forming a decagon.

How many triangles can be formed by joining them?

Answer 1

Number of vertices in a decagon $=10$.

From these vertices, we will choose $3$ vertices to form a triangle.

Hence, number of ways to do this ${=}^{10}{C}_3=\frac{10!}{3!\cdot 7!}=\frac{10\times 9\times 8}{3\times 2\times 1}=120$ triangles