NSW Y11 Maths - Extension 1 Permutations and Combinations Counting Principle

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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/

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

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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 \( \to p \times q = 4 \times 3 = 12\)