MathematicsChapter 6: Permutation and Combination
Exam Response (permutations and Combinations)
Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions.
Learning objectives
- 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.
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 the product or the nCr. Cancel factorials on the page.
Where / symbols
- 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'.
Overview
Classify, then compute:
Classify
Line up / ranks -> nPr. Committee -> nCr. Round table -> (n-1)!. Together -> block. PIN with order -> product rule.
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'.
Examples 7P3=7*6*5 · 8C3=56 · 4! * 2 for a pair together
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)
How to answer a exam response (permutations and combinations) question
- 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.
Worked example
- Worked 4-mark: 4-letter codes from ABCDE, no repeat.
- order matters, no repeat
- 5P4 = 5*4*3*2 = 120
- not 5C4 (that would ignore order)
In simple words
The word 'arrange' is permutation. The word 'select' is combination.
Key points
- order? permutation : combination
- circle: (n-1)!
- one label
- cancel
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Exam Response (permutations and Combinations)
Sticky Notes · Quick Revision
Core Idea
- Typical tasks: n!, nPr, nCr, circular (n-1)!, together/not together, committee with restrictions.
- First decide: does order matter?
- Line vs circle?
1. CLASSIFY
- Line up / ranks -> nPr.
- Committee -> nCr.
- Round table -> (n-1)!.
- Together -> block.
2. COMPUTE
- Write n(n-1)...
- or nCr as a cancelled fraction.
- 0!=1.
- nCr=nC(n-r).
Worked Example
- Worked 4-mark: 4-letter codes from ABCDE, no repeat.
- order matters, no repeat
- 5P4 = 5*4*3*2 = 120
- not 5C4 (that would ignore order)
Common Misconception
- The word 'arrange' is permutation. The word 'select' is combination.
FBISE Exam Check
- State the rule for exam response (permutations and combinations) before substituting values.
- Show the main algebra steps, keep exact values where possible, and check every condition.
60-second revision
- 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.
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