Maths Extension 1 Year 11 - Module 4 - Lesson 5
Circular Permutations
Name
Date
Class
1. Lesson focus
Circular permutations. For n distinct people around an unlabelled round table, rotations count as the same arrangement, giving (n−1)! arrangements; clockwise and reflected arrangements count as different.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. How many circular arrangements of 7 distinct people are there?
3. Six people sit around a table. A and B must sit together. How many arrangements?
3. Challenge
Eight people sit around a table. How many arrangements have A and B not adjacent?
4. Multiple choice
The number of circular arrangements of 6 distinct people is what?
A. 2×5!=240
B. 6!=720
C. 4!=24
D. 5!=120
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. How many ways can 5 people sit around a round table?
(5−1)!=4!=24.
2. How many circular arrangements of 7 distinct people are there?
(7−1)!=6!=720.
3. Six people sit around a table. A and B must sit together. How many arrangements?
Group A/B as one unit: 5 units around a circle give 4! orders; the pair can swap, so 2×4!=48.
Challenge. Eight people sit around a table. How many arrangements have A and B not adjacent?
Total 7!=5040. Adjacent: pair block gives 6!×2=1440. Not adjacent: 5040−1440=3600.
Multiple choice. The number of circular arrangements of 6 distinct people is what?
Correct answer: D. Fix one person to remove rotational duplicates; arrange the remaining five in 5! ways.
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