You are the head Director of your company and you want to create an 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-

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

Next, after your group is selected, you want them to take a 10 problem questionnaire, which will show you how in- tuned your group is with the company at present day. The 10-problem questionnaire will consist of four multiple-choice answers where only one is correct. What is the probability that the group would have no less than two correct? Explain if this sort of process would be beneficial or not to your endeavors for the company. Be thorough in your explanations.