Question

How many triangles can be formed by joining the vertices of a decagon?

Answer 1

Since decagon has $10$ sides, clearly $10$ vertices of
decagon say $A_1,A_2,A_3,...,A_{10}$. Also triangle is formed by
three points which are not collinear.
Hence number of triangles by joining the vertices of decagon is ${=}^{10}{C}_3=\frac{\mathrm{10.9.8}}{\mathrm{1.2.3}}=120$