Question

The department in which you work in your company has 24 employees: 10 women and 14 men. A team of 4 employees must be selected to represent the department at a companywide meeting in the headquarters of the company. The team must have two women and two men. How many different teams of 4 can be selected

Answer 1

We conclude that 4095 different teams can be selected.

Explanation:

We know that a company has 24 employees: 10 women and 14 men.

A team of 4 employees must be selected. The team must have two women and two men.

So from 10 women we choose 2 women:

`C_2^(10)=(10!)/(2!(10-2)!)=45\\`

So from 14 men we choose 2 men:

`C_2^(14)=(14!)/(2!(14-2)!)=91\\`

We get: 45 · 91 = 4095.

We conclude that 4095 different teams can be selected.