16. (15 points) There are 4 bookstores that together ordered 400 copies of the magazine "Mathematical World". Each bookstore ordered at least 98 copies and at most 101 copies. How many different ways can this be done?

保留源文本的换行和格式，翻译结果如下：

16. (15 points) There are 4 bookstores that together ordered 400 copies of the magazine "Mathematical World". Each bookstore ordered at least 98 copies and at most 101 copies. How many different ways can this be done?
【Solution】Solution: First, distribute 98 books to each bookstore, leaving 8 books. The problem is then transformed into distributing 8 books to 4 bookstores, with each bookstore receiving 0, 1, 2, or 3 books,

Possible distribution scenarios are:
$$
\left\{\begin{array}{l}
3,3,2,0 \\
3,3,1,1 \\
3,2,2,1 \text { these } 4 \text { types, } \\
2,2,2,2
\end{array}\right.
$$
(1) For the distribution 3, 3, 2, 0, there are $C_{4}^{2} \times C_{2}^{1}=12$ ways,
(2) For the distribution 3, 3, 1, 1, there are $C_{4}^{2}=6$ ways,
(3) For the distribution 3, 2, 2, 1, there are $C_{4}^{1} \times C_{3}^{2}=12$ ways,
(4) For the distribution 2, 2, 2, 2, there is 1 way,

Therefore, there are a total of: $12+6+12+1=31$ ways,
There are a total of 31 different ways to order.