Specialist Mathematics · Unit 1 · Combinatorics · Introduction to counting techniques
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A school committee has 12 members: 5 from the Arts faculty and 7 from the Science faculty. A subcommittee of 4 members must be formed. Determine the number of possible subcommittees that contain exactly 2 members from Arts OR exactly 3 members from Science. Use the addition principle in your solution.
A school library is selecting 4 books to display in a showcase. The library has 9 fiction books and 6 non-fiction books available. The showcase must contain books that are either all fiction or all non-fiction. Use the addition principle to determine the number of different displays that can be created.
Use the addition principle to determine the number of ways a student can choose exactly one elective subject from the following options: • three different science subjects • four different humanities subjects • two different technology subjects.
A school offers three mathematics subjects: Mathematical Methods, Specialist Mathematics, and General Mathematics. The table below shows the number of Year 12 students enrolled in each subject and the number of students enrolled in combinations of subjects. Determine the total number of Year 12 students enrolled in at least one mathematics subject.
Use the addition principle to determine the number of ways a student can select exactly one book from the shelves shown in the diagram below. The top shelf contains mathematics books and the bottom shelf contains physics books.
A school committee has 9 members: 5 from the Science department and 4 from the Arts department. A subcommittee of 3 members is to be formed such that it contains at least one Science member or at least two Arts members (or both). Use the addition principle to calculate the number of possible subcommittees.
A committee of 12 people consists of 5 engineers and 7 scientists. A working group of 4 people must be selected from the committee. Use the addition principle to determine how many different working groups can be formed that include at least 2 engineers but fewer than 3 scientists.
A student council has 15 members: 7 from Year 11 and 8 from Year 12. A delegation of 3 students must be selected to attend a conference. The delegation must include at least one student from Year 11 AND at least one student from Year 12. Use the addition principle to determine the number of possible delegations.
A sports club has 9 members who play tennis and 11 members who play badminton. No member plays both sports. The club needs to select a team of 4 members to represent the club at a tournament. The team must consist entirely of tennis players OR entirely of badminton players. Use the addition principle to determine the number of possible teams.