N2026 P2 Q6

The employees of a certain company are put into teams based on the jobs that they do. The company consists of \(22\) employees from the Red team, \(18\) from the Blue team, \(9\) from the Green team and \(6\) from the Yellow team.

The manager of the company wishes to find out the opinions of the employees about the office facilities provided for employees. Questionnaires are given to all employees but only the \(40\) employees from the Red team and the Blue team return them.

1. Explain whether these \(40\) employees comprise a sample or a population.[1]

The manager decides to form a committee of employees to discuss the results of the questionnaire.

2. State an advantage of choosing a random sample of employees for the committee.[1]

The manager decides that the committee will consist of \(5\) employees, such that

• the committee includes an employee from the Green team,
• at least three teams are represented on the committee and
• there are more members from the Red team than from any other single team on the committee.

3. Find the number of ways in which the committee can be formed.[4]