1 Counting Principles 1a. [1 mark] Twelve students are to take an exam in advanced combinatorics. The exam room is set out in three rows of four desks, with the invigilator at the front of the room, as shown in the following diagram. INVIGILATOR Find the number of ways the twelve students may be arranged in the exam hall. 1b. [2 marks] Two of the students, Helen and Nicky, are suspected of cheating in a previous exam. Find the number of ways the students may be arranged if Helen and Nicky must sit so that one is directly behind the other (with no desk in between). For example Desk 5 and Desk 9. 1c. [3 marks] Find the number of ways the students may be arranged if Helen and Nicky must not sit next to each other in the same row. 2a. [2 marks] From a group of five males and six females, four people are chosen. Determine how many possible groups can be chosen. 2b. [2 marks] Determine how many groups can be formed consisting of two males and two females.