Question:
How many triangles can be formed in a decagon?
Solution:
Total number of sides in a decagon = 10
We know that number of vertices in triangle $=3$
So, out of 10 vertices we have to choose 3 vertices.
Therefore,
Total number of triangles in a decagon $={ }^{10} \mathrm{C}_{3}$ $=\frac{10 !}{3 ! \times(10-3) !}=\frac{10 \times 9 \times 9}{3 \times 2}$
Total number of triangles = 120