Example 3-3 $S=\{1,2,3, \cdots, 600\}$, find the number of elements in it that are divisible by $2,3,5$.
Let $A, B, C$ represent the numbers in $S$ that are divisible by $2, 3, 5$ respectively.
$$
\begin{array}{l}
|A|=\left\lfloor\frac{600}{2}\right\rfloor=300, \quad|B|=\left\lfloor\frac{600}{3}\right\rfloor=200, \\
|C|=\left\lfloor\frac{600}{5}\right\rfloor=120, \quad|A \cap B|=\left\lfloor\frac{600}{2 \times 3}\right\rfloor=100, \\
|A \cap C|=\left\lfloor\frac{600}{10}\right\rfloor=60, \quad|B \cap C|=\left\lfloor\frac{600}{15}\right\rfloor=40 \\
|A \cap B \cap C|=\left\lfloor\frac{600}{30}\right\rfloor=20 \\
|A \cup B \cup C|=|A|+|B|+|C| \\
-(|A \cap B|+|A \cap C|+|B \cap C|)+|A \cap B \cap C| \\
=300+200+120-(100+60+40)-20=400 \\
\end{array}
$$

Similarly, we can derive
$$
\begin{aligned}
|A \cup B \cup C \cup D|= & |A|+|B|+|C|+|D| \\
& -|A \cap B|-|A \cap C|-|A \cap D|-|B \cap C|-|B \cap D|-|C \cap D| \\
& +|A \cap B \cap C|+|A \cap B \cap D|+|B \cap C \cap D| \\
& -|A \cap B \cap C \cap D|
\end{aligned}
$$

In general,