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Exam Response (permutations and Combinations)
Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions. First decide: does order matter? Line vs circle? Then write the product or the nCr. Cancel factorials on the page.
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Exam Response (permutations and Combinations)
What is it?
Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions. First decide: does order matter? Line vs circle? Then write the product or the nCr. Cancel factorials on the page.
In simple words
- Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions.
- First decide: does order matter?
- Line vs circle?
- The word 'arrange' is permutation. The word 'select' is combination.
Important terms
EXAM RESPONSE (PERMUTATIONS AND COMBINATIONS): Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions. First decide: does order matter? Line vs circle? Then write the product or the nCr. Cancel factorials on the page.
1. CLASSIFY: Line up / ranks -> nPr. Committee -> nCr. Round table -> (n-1)!. Together -> block. PIN with order -> product rule.
2. COMPUTE: Write n(n-1)... or nCr as a cancelled fraction. 0!=1. nCr=nC(n-r). Show the case split for 'at least'.
What you should learn
- State the main ideas and notation used in exam response (permutations and combinations).
- Apply the rules of exam response (permutations and combinations) in a clear, step-by-step solution.
- Check signs, conditions, and the final answer for mathematical accuracy.
Examples
- Order yes/no
- Circle yes/no
- Glue or complement
CLASSIFY
Line up / ranks -> nPr. Committee -> nCr. Round table -> (n-1)!. Together -> block. PIN with order -> product rule.
COMPUTE
Write n(n-1)... or nCr as a cancelled fraction. 0!=1. nCr=nC(n-r). Show the case split for 'at least'.
Recommended for Class 11
Full school-level explanation
Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions. First decide: does order matter? Line vs circle? Then write the product or the nCr. Cancel factorials on the page.
Classify, then compute:
WHAT — EXAM RESPONSE (PERMUTATIONS AND COMBINATIONS)
Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions. First decide: does order matter? Line vs circle? Then write the product or the nCr. Cancel factorials on the page.
RULE — 1. CLASSIFY
Line up / ranks -> nPr. Committee -> nCr. Round table -> (n-1)!. Together -> block. PIN with order -> product rule.
METHOD — 2. COMPUTE
Write n(n-1)... or nCr as a cancelled fraction. 0!=1. nCr=nC(n-r). Show the case split for 'at least'.
WORKED EXAMPLE
Worked 4-mark: 4-letter codes from ABCDE, no repeat. order matters, no repeat 5P4 = 543*2 = 120 not 5C4 (that would ignore order)
CLASSIFY
Line up / ranks -> nPr. Committee -> nCr. Round table -> (n-1)!. Together -> block. PIN with order -> product rule.
Remember
- one label
Examples
- Order yes/no
- Circle yes/no
- Glue or complement
COMPUTE
Write n(n-1)... or nCr as a cancelled fraction. 0!=1. nCr=nC(n-r). Show the case split for 'at least'.
Remember
- cancel
Examples
- 7P3=7*6*5
- 8C3=56
- 4! * 2 for a pair together
How to answer a exam response (permutations and combinations) question
How it works
- Identify the given quantities, notation, and required result.
- Choose the matching rule and write it before substitution.
- Work one algebraic step at a time, keeping brackets and signs clear.
- Check restrictions, simplify the result, and verify it where possible.
Remember
- order? permutation : combination
- circle: (n-1)!
- 120
- arrange vs select
- one label
- cancel
- order? permutation : combination
- circle: (n-1)!
How the ideas connect
Worked 4-mark: 4-letter codes from ABCDE, no repeat. order matters, no repeat 5P4 = 543*2 = 120 not 5C4 (that would ignore order)
Deeper understanding
Go beyond memorising Exam Response (permutations and Combinations). Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked 4-mark: 4-letter codes from ABCDE, no repeat. order matters, no repeat 5P4 = 543*2 = 120 not 5C4 (that would ignore order)
Common mistakes
Exam focus
Core Idea
1. CLASSIFY
2. COMPUTE
Worked Example
Exam focus
Quick revision
- order? permutation : combination
- circle: (n-1)!
- 120
- arrange vs select
- EXAM RESPONSE (PERMUTATIONS AND COMBINATIONS): Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions. Fi
- 1. CLASSIFY: Line up / ranks -> nPr. Committee -> nCr. Round table -> (n-1)!. Together -> block. PIN with order -
The word 'arrange' is permutation. The word 'select' is combination.
For long answers on Exam Response (permutations and Combinations): define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- order? permutation : combination
- circle: (n-1)!
- 120
- arrange vs select
Important formulas
- order? permutation : combination
- circle: (n-1)!
- 120
Common exam traps
- The word 'arrange' is permutation. The word 'select' is combination.
- Do not use a remembered formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
The word 'arrange' is permutation. The word 'select' is combination.
- Mistake
Do not use a remembered formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes or restrictions; write them on the line where they are used.
- Mistake
The word 'arrange' is permutation. The word 'select' is combination.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
order? permutation : combination
circle: (n-1)!
120
arrange vs select
Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions. First decide: does order matter? Line vs circle? Then write th
- Definition
- Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions. First decide: does order matter? Line vs circle? Then write th
- Example
- Order yes/no
- Critical warning
- The word 'arrange' is permutation. The word 'select' is combination.
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Exam Practice
Define
Q1. Define Exam Response (permutations and Combinations).
Explain
Q2. Explain: CLASSIFY.
Example
Q3. Give one clear example of Exam Response (permutations and Combinations) and say why it fits.
Mistake
Q4. State one common mistake students make about Exam Response (permutations and Combinations).
Exam note
Q5. Write a short exam note on Exam Response (permutations and Combinations): definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.