NSW Y11 Maths - Extension 1 Permutations and Combinations Counting Principle

Resources for Counting Principle

  • Questions

    9

    With Worked Solution
    Click Here
  • Video Tutorials

    1


    Click Here

Counting Principle Theory

NSW Syllabus Reference

NSW Syllabus Reference: ME-A1.1: Permutations and combinations. This will require student to 

  • list and count the number of ways an event can occur
  • use the fundamental counting principle (also known as the multiplication principle)
  • use factorial notation to describe and determine the number of ways 𝑛 different items can be arranged in a line or a circle
  • solve simple problems and prove results using the pigeonhole principle (ACMSM006)
  • understand and use permutations to solve problems (ACMSM001)
  • solve problems involving permutations and restrictions with or without repeated objects (ACMSM004)
  • understand and use combinations to solve problems (ACMSM007)
  • solve practical problems involving permutations and combinations, including those involving simple probability situations

Ref: https://educationstandards.nsw.edu.au/

Create account

Access content straight away with a two week free trial

I am..

Please enter your details

I agree with your terms of service




Videos

Videos relating to Counting Principle .

  • Counting Principle - Video - Arrangements of objects in a row

    You must be logged in to access this resource

Plans & Pricing

With all subscriptions, you will receive the below benefits and unlock all answers and fully worked solutions.

  • Teachers Tutors
    Features
    Free
    Pro
    All Content
    All courses, all topics
     
    Questions
     
    Answers
     
    Worked Solutions
    System
    Your own personal portal
     
    Quizbuilder
     
    Class Results
     
    Student Results
    Exam Revision
    Revision by Topic
     
    Practise Exams
     
    Answers
     
    Worked Solutions
  • Awesome Students
    Features
    Free
    Pro
    Content
    Any course, any topic
     
    Questions
     
    Answers
     
    Worked Solutions
    System
    Your own personal portal
     
    Basic Results
     
    Analytics
     
    Study Recommendations
    Exam Revision
    Revision by Topic
     
    Practise Exams
     
    Answers
     
    Worked Solutions

Theory

If an outcome can happen in \(p\) different ways and a second outcome can happen in \(q\) different ways, then the total number of ways in which the two ways can happen together is \(p \times q\) different ways.

For example: If there are 4 ways of travelling from town A to town B and 3 ways of travelling from town B to town C, what are the total number of ways of travelling from town A to town C through town B?

Let \(p=\) ways from A to B \( \to p = 4\)

Let \(q=\) ways from B to C \( \to q = 3\)

The number of total ways from A to B to C \( \to p \times q = 4 \times 3 = 12\)