2026 HCI P2 Q5

A product development company requires 12 of its employees, consisting of 3 employees from the Engineering department, 4 employees from the Marketing department and 5 employees from the Programming department, to do a presentation at a new product launch.

1. Before the launch starts, the employees are seated in a row such that the 3 employees from the Engineering department must be separated and the 4 employees from the Marketing department must be together. Find the number of ways in which the 12 employees can be seated.[2]

After their presentations, 4 employees are selected for a Q&A session.

2. Find the number of ways to select the 4 employees for the Q&A session without any restrictions.[1]
3. Find the probability that the Q&A session consists of at least one employee from each of the three departments.[2]
4. After the launch and Q&A session, all the 12 employees proceed to a celebratory dinner. They are seated at a round table. Find the probability that there are exactly 2 employees between two particular employees from the Marketing department.[2]