Mixed Problems: Permutations vs. Combinations
Develop the critical skill of analysing complex counting problems to determine whether the situation calls for permutations, combinations, or a combination of both principles.
About This Topic
Develop the critical skill of analysing complex counting problems to determine whether the situation calls for permutations, combinations, or a combination of both principles.
Key Questions
- Analyse a word problem to identify keywords that suggest whether order matters or not.
- Compare the solution for selecting a president, vice-president, and treasurer with that of selecting a 3-person committee.
- Explain the steps to solve a problem that involves both selection and arrangement, such as forming a team and then assigning positions.
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Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Permutations and Combinations
Permutations: When Order Matters
Define permutations as ordered arrangements, understand and use factorial notation, and apply the formula P(n, r) to calculate the number of possible arrangements of objects.
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Permutations with Specific Conditions
Solve more complex arrangement problems, such as when some of the objects to be arranged are identical or when there are specific restrictions on the positions of certain objects.
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