Let $n \geq 3$ be an integer. Let $P_1, P_2, \ldots, P_{2 n}$ be points in the plane, which are the vertices of a regular $2 n$-gon. The number of obtuse-angled triangles with vertices contained in the set $\left\{P_1, P_2, \ldots, P_{2 n}\right\}$ is

• Correct answer
  A

  $n(n-1)(n-2)$
• B

  $\frac{n^2(n-1)(n-2)}{3}$
• C

  $\frac{n(n-1)^2}{2}$
• D

  $2 n(2 n-1)(2 n-2)$

Hence, the correct answer is option: 'A'.