We have a population of people (denoted by S=30000). Assume that we want to divide this population into groups (denoted by D) consisting eight (8) and only eight (8) teams (denoted by C) of four(4) members from the population with the following conditions:

a) none of those teams is participating in more than one group; in other words, a particular team, participating in one group, must not participate in any other groups at a same time.

b) teams participating in a particular group must not have any team members in common; however it is possible for different groups to enjoy of teams with common members - in fact, it is allowed for teams to have common members in general but those teams participating in a particular group must not have any team member in common.

c) permutation of members in a team is not important - teams consisting of {m1, m2, m3, and m4} or {m4, m2, m1, m3} are considered as one particular team

d) it is important how teams are arranged in a group - permutation of teams is important i.e. if teams in group D1 arranged like T1-T2-T3...-T8 means team T1 is working with T2 and team T2 is working with T3 and thus the resulting group differs if the teams would be arranged like T3-T1-T2-...-T8

Appreciate if you recommend a mathematical model for this calculation; also if my numbers are big then you may recommend me a free appropriate software for the probability calculation.

Best,

David