Maths Extension 1 Year 11 - Module 4 - Lesson 15
Mixed Combinatorics & Exam Technique
Name
Date
Class
1. Lesson focus
Mixed combinatorics and exam technique. Decide whether the task is an ordered arrangement, an unordered selection, a circular arrangement or a restricted count before choosing a formula.
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. Assign gold, silver and bronze among 8 finalists. How many outcomes?
3. How many ways can 5 distinct people sit around a round table?
3. Challenge
Six distinct books are arranged with two specified books adjacent. How many arrangements?
4. Multiple choice
When order matters in choosing r objects from n distinct objects, which expression applies?
A. n+r
B. nCr=n!/[r!(n−r)!]
C. n!−r!
D. nPr=n!/(n−r)!
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Choose 3 students from 8 for a team. How many teams?
8C3=56.
2. Assign gold, silver and bronze among 8 finalists. How many outcomes?
8P3=8×7×6=336.
3. How many ways can 5 distinct people sit around a round table?
(5−1)!=24.
Challenge. Six distinct books are arranged with two specified books adjacent. How many arrangements?
Treat the pair as a block: 5!×2=240.
Multiple choice. When order matters in choosing r objects from n distinct objects, which expression applies?
Correct answer: D. Ordered selections use permutations; combinations divide by r! because internal order does not create a new selection.
Want help with Worksheet - Mixed Combinatorics & Exam Technique?
Tell us what you would like help with. Register interest; support details will be confirmed before enrolment.
Register interest →