NSW Y11 Maths - Extension 1 Permutations and Combinations Pigeonhole Principle

Resources for Pigeonhole Principle

  • Questions

    9

    With Worked Solution
    Click Here
  • Video Tutorials

    1


    Click Here
  • HSC Questions

    2

    With Worked Solution
    Click Here

Pigeonhole 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

I am..

Please enter your details

I agree with your terms of service




Videos

Videos relating to Pigeonhole Principle.

  • Pigeonhole Principle - Video - Pigeonhole Principle Proof

    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

The pigeonhole principle is a way of finding how a number of items can be placed in a number of containers.

For example: If you have ten pigeons in nine pigeonholes, then one of the pigeonholes must contain at least two pigeons. In general if \((n + 1)\) items occupy \(n\) containers, then at least one of the containers must contain at least two items. For \(n > k\) if \(n\) items are sitting in \(k\) containers then there is at least one container with at least \(\dfrac{n}{k}\) items in it.

For example: There are ten pigeons sitting in six pigeonholes. What is the least number of pigeons to occupy one pigeonhole?

\(n = 10,\,k = 6 \to \dfrac{n}{k} = {\mathop{\rm int}} \left( {\dfrac{{10}}{6}} \right) = 2\). Hence there must be at least 2 pigeons to occupy one pigeonhole.