This is a limited distance combination problem, where $n=30, k=3, m=8$, so there are different arrangement methods
$$
C_{30-7 \times 2}^{3}=C_{16}^{3}=560 \text { (ways) }
$$
【Example 2】A school plans to arrange 3 math lectures in September, with at least 7 days between any two lectures. How many ways are there to arrange the lectures?