NSW Y11 Maths - Extension 1 Permutations and Combinations Combinations

Resources for Combinations

  • Questions

    38

    With Worked Solution
    Click Here
  • Video Tutorials

    1


    Click Here
  • HSC Questions

    5

    With Worked Solution
    Click Here

Combinations 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

I am..

Please enter your details

I agree with your terms of service




Videos

Videos relating to Combinations.

  • Combinations - Video - Combinations made easy

    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

A combination is an unordered permutation of all or part of a set of objects.

An example is to win games of chance like Lotto where it does not matter in which order that the numbers arise but only that the correct group has been selected.

The notation used is \({}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}\)

For example: Six people are available to play tennis. A group of four is chosen to play. In how many ways can this be done?

\({}^6{C_4} = \dfrac{{6!}}{{4!(6 - 4)!}} = 15\) also using the \({}^n{C_r}\) symbol on your calculator.