Permutation and combination  (14.114.3)
Understand the addition rule and multiplication rule in the counting principle

Theory

Examplesa) In S5A, students must choose to study at least one subject between History and Geography.
There are 38 students in the class, 30 of them study History and 27 of them study Geography.
How many students in S5A study both History and Geography?
b) In S5A, S5B and S5C, there are 8 students, 10 students and 13 students respectively who are
qualified to join a competition. If 3 qualified students are selected, how many ways are there to
select one student from each class?

Solutionsa) Let x be the number of students in S5A study both History and Geography.
\(\begin{array}{c}38 = 30 + 27  x\\x = {19^{}}\end{array}\)
Therefore, 19 students in S5A study both History and Geography.
b)Number of ways
\(\begin{array}{l} = 8 \times 10 \times 13\\ = {\underline{\underline {1{\rm{ }}040}} ^{}}\end{array}\)