Maths Extension 1 Year 11 - Module 4 - Lesson 1
Introduction to Combinatorics & Counting Principles
Name
Date
Class
1. Lesson focus
Counting principles and arrangements. Use the product rule for sequential choices; for n distinct objects arranged in a row there are n! orders.
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 5-digit codes can be formed from digits 1,2,3,4,5 without repetition?
3. A school chooses a president, vice-president and treasurer from 8 students. How many outcomes?
3. Challenge
How many distinct arrangements are there of the letters in MATHS?
4. Multiple choice
The number of linear arrangements of 6 distinct objects is what?
A. 5!=120
B. 6×5=30
C. 6²=36
D. 6!=720
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. How many ways can 4 distinct books be arranged on a shelf?
4!=24 arrangements.
2. How many 5-digit codes can be formed from digits 1,2,3,4,5 without repetition?
There are 5×4×3×2×1=5!=120 codes.
3. A school chooses a president, vice-president and treasurer from 8 students. How many outcomes?
Roles are distinct: 8×7×6=8P3=336.
Challenge. How many distinct arrangements are there of the letters in MATHS?
All 5 letters are distinct, so 5!=120.
Multiple choice. The number of linear arrangements of 6 distinct objects is what?
Correct answer: D. Each of the six objects can be first, then five choices remain, giving 6×5×4×3×2×1=720.
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