Long answer·Hard exam skill (4/5)·No calculatorNeeds mentor review
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Question
A shelf has distinct mathematics books and distinct science books.
Total: 5 marks
(a) In how many ways can all books be arranged if the science books must stay together? (2 marks)
(b) In how many ways can books be selected with exactly mathematics and science books? (2 marks)
(c) In how many ways can two distinct books be assigned to first and second display positions? (1 mark)
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