2001 CMO 第 5 题

Let $P_1P_2\ldots P_{24}$ be a regular $24$ -sided polygon inscribed in a circle $\omega$ with circumference $24$ . Determine the number of ways to choose sets of eight distinct vertices from these $24$ such that none of the arcs has length $3$ or $8$ .

令 $P_1P_2\ldots P_{24}$ 为内接于圆周 $24$ 的圆 $\omega$ 的规则 $24$ 边多边形。确定从这些 $24$ 中选择八个不同顶点的集合的方法数，使得没有弧具有长度 $3$ 或 $8$ 。