# Isn't it simple counting?

Discrete Mathematics Level 4

Let $$A_{1}A_{2}A_{3}A_{4}.....A_{21}$$ be a 21-sided regular polygon inscribed in a circle with centre $$O$$. How many triangles $$A_{i}A_{j}A_{k}$$, $$0<i<j<k<22$$, contain the point $$O$$ in their interior.

NOTE: This is not an original problem

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