I really need help with the following problem:
A company contains three managers, two accountants, one CFO, and one CEO. The roles need to filled from a group of 11 men and 10 women. The workforce must be composed of 4 men and 3 women. If you choose a particular 7 employees, changing their positions is considered to change the team. But a manager is a manager and an accountant is a accountant, so swapping the two managers, for example, does not change the company.
(a) How many different teams are possible if each person can play any position? (b) How many different teams are possible if 3 of the 11 men only know how to be CEOs? (c) How many different teams are possible if each person can be any role, but Jessica, Marnie (women) and Ryan (man) cannot all be chosen because they talk too much when placed on the same team. (Two of the three may be placed on the work team, but not all three at once).
I really have no idea where to start with this problem. My first instinct for part (a) was to add C(11,4) + C(10,3) = 450 combinations. But that number seems too low. What about the rest? Sorry if this is obvious I'm just brand new to this type of math.