【Example 6】There are three types of books, 50 copies each, placed on three levels of a bookshelf, with each level holding one type. How many ways are there to arrange them?
Here are two levels of compound permutations: First, which type of books is placed on which level, which is a full permutation of 3 elements; second, the placement within each type of books also involves a permutation process. Therefore, according to the multiplication principle, there are
$$
A_{3}^{3} \cdot A_{50}^{50} \cdot A_{50}^{50} \cdot A_{50}^{50}=3!\cdot(50!)^{3}=6 \cdot(50!)^{3}
$$

different ways to place the books.