2018 HCI JC2 CT1 Q9 (a)

In a particular college, students must choose 4 subjects to read.Subjects are classified as either ‘Arts’ or ‘Science’.The available ‘Arts’ subjects are Economics, Geography, History and Literature, and the available ‘Science’ subjects are Biology, Chemistry, Mathematics and Physics.Each student must read at least one ‘Arts’ subject and at least one ‘Science’ subject.

1. Find the number of ways that a student can choose his 4 subjects.[2]

The subjects are further classified into 2 levels, H1 and H2. Each student must read 3 subjects at H2 level and 1 subject at H1 level, and he cannot read the same subject at both H1 and H2 levels.

2. Find the number of ways that a student can choose his 3H2 and 1H1 subjects.[1]

In addition to the rules above, a student who reads H2 Biology, H2 Chemistry or H2 Physics must also read H2 Mathematics.

3. Find the number of ways that a student can choose his 3 H2 and 1 H1 subjects with this additional rule.[3]