计算排列的数量
嘿，我正在学习 DS&A 课程，我们有一个关于计算排列的有趣的作业问题。问题如下：
有 N(N <= 15) 个人，每个人的 id 从 1 到 N。所有 N 个人都有一个他们愿意接受的号码列表。您有一个大小为 N 个数字的数组，称为 A。您可以随意排列A。对于每个排列，A 中的第一个数字属于第一个人，第二个数字属于第二个人，依此类推。对于每个人来说，A 的排列数是多少，A 中分配给他们的数字也在他们的列表中？
我曾尝试考虑使用有向图，但无法弄清楚。有人能指出我正确的方向吗？
谢谢！
Hey I'm taking a DS&A course, and we had an interesting homework question regarding counting permutations. The problem is the following:
There is are N(N <= 15) people each with an id from 1 to N. All N people have a list of numbers they will accept. You have an array of size N numbers called A. You can permutate A however you like. For each permutation, the first number in A goes to the first person, the second number goes to the second person, and so on. What is the number of permutations of A where, for every person, their assigned number in A is also in their list?
I've tried thinking about using directed graphs, but couldn't figure it out. Could someone point me in the right direction?
Thanks!
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