You are the head Director of your company, and you want to create a think-tank, which can provide ideas for the future of the company. However, you want your company to be diverse through gender representation.  You must be a part of the group and each department will be allowed so many representatives. Management can have no more than 2 people, and mid-management can have no more than four people, but no less than two. The labor force will have no more than 5 but no less than 3 representatives in the group. How many different ways can a group of 10 be combined with the cohorts of people listed below with no gender having less than 25 percent representation?
Management
Head Director- Female
Director 2- Male
Director 3- Female
 
Mid- Management
Supervisor 1- Male
Supervisor 2- Female
Supervisor 3- Female
Supervisor 4- Male
Supervisor 5- Male
 
Labor Force
Worker 1- Male
Worker 2- Female
Worker 3- Female
Worker 4- Female
Worker 5- Male
Worker 6- Male
Worker 7- Female
Worker 8- Male
Worker 9- Female
Worker 10- Male