how to compute this permutation problem?

Thanks firstly! : )

Now we have n persons $$n_1,n_2,n_3,n_4...$$. for each person, he have written 2 kinds of articles: A B.
For example, for person $$n_2$$, there are some articles A and B. We will compare each A of person $$n_2$$ with each B of person $$n_1$$,$$n_3$$,$$n_4$$,$$n_5$$.... For $$n_2$$ himself, A articles and B articles (we call them $$A_2[_1]$$,$$A_2[_2]$$,$$A_2[_3]$$...,$$B_2[_1]$$,$$B_2[_2]$$..., first subscript means person number, $$A_2$$ means all A articles for person $$n_2$$. second means article number) will have some similarity (we have evaluation standard for this, you can call it one standard value $$S$$).

We say it's one $$F$$ event if the similarity of $$A_2[_1]$$ and $$B_1[_2]$$ is bigger than $$S$$ (note that $$A_2$$ and $$B_1$$ are different persons). If it's smaller than S, we call it as $$T$$ event.

We use $$M(n_1,n_2)$$ to represent number of $$F$$ event between $$A_1$$ with $$B_2$$, use $$N(n_1,n_2)$$ to represent number of comparing between $$A_1$$ with $$B_2$$ (we know that it's number of $$A_1$$ multiply number of $$B_2$$).

We use $$M(n_2,n_1)$$ to represent number of $$F$$ event between $$A_2$$ with $$B_1$$. use $$N(n_2,n_1)$$ to represent number of comparing between $$A_2$$ with $$B_1$$ (we know that it's number of $$A_2$$ multiply number of $$B_1$$).

I can get all $$M(n_x,n_y)$$ values and $$N(n_x,n_y)$$. Now, I need select 5 persons from n persons randomly (use $$C^5_n$$ to enumerate all possible situations) and compare all 5 persons' A articles and all other persons' B articles.

I want compute that :

for each combination in $$C^5_n$$ , I need to get $$M(n_yn_xn_dn_en_u, n_z)$$/$$N(n_yn_xn_dn_en_u, n_z)$$. here $$y,x,d,e,u$$ will construct $$C^5_n$$ and $$z$$ means other person.

ps: I can enumerate all $$C^5_n$$ situations, and computate all $$M$$ and $$N$$, but when number of persons are big, it's so big for compuater to simulate.