One question decides everything in this topic: does the order matter? If it does you want a permutation, if it doesn't you want a combination, and almost every lost mark traces back to answering that question wrongly.
Syllabus points covered
- Recognise and distinguish between permutations and combinations
- Evaluate nPr and nCr and use them in problems
- Solve problems about arrangements of objects in a line, including repetition and restriction
- Solve problems about selections from a set
Common mistakes
- Using a permutation for a selection where order is irrelevant, such as choosing a committee.
- Handling 'at least' conditions by adding cases incorrectly — often it's quicker to count the complement.
- Forgetting to divide by the factorials of repeated letters when arranging a word with repeats.
- Treating a restriction like 'two people must sit together' as separate when they should be blocked as one unit first.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers