Question

An employee group requires seven people be chosen for a committee from a group of 18 employees. Determine the following probabilities of a randomly drawn committee of seven employees.

An employee group has six women and 12 men. What is the probability that three of the people chosen for the committee are women and four people chosen for the committee are men ?
The committee requires that exactly 2 people from customer service serve on the committee. There are 4 people in customer service. What is the probability that exactly 2 of the people chosen for the committee are from customer service? Use combinations to solve.

Answer 1

To calculate the probabilities, we can use the concept of combinations.

Probability of choosing 3 women and 4 men:

First, let's calculate the total number of possible committees of 7 people out of 18 employees:

Total number of committees = C(18, 7)

Now, let's calculate the number of committees with 3 women and 4 men:

Number of committees with 3 women and 4 men = C(6, 3) * C(12, 4)

The probability can be calculated as:

Probability = (Number of committees with 3 women and 4 men) / (Total number of committees)

Probability of choosing exactly 2 people from customer service:

The number of ways to choose 2 people from customer service is C(4, 2). We also need to choose 5 people from the remaining employees (18 - 4 = 14). The number of ways to choose 5 people from the remaining employees is C(14, 5). Therefore, the total number of committees with exactly 2 people from customer service is:

Number of committees with 2 people from customer service = C(4, 2) * C(14, 5)

The probability can be calculated as:

Probability = (Number of committees with 2 people from customer service) / (Total number of committees)

Note: In both cases, the total number of committees is the same, which is C(18, 7).

Now you can calculate the probabilities using the formulas provided.