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NSW Y11 Maths Standard NSW Y11 Maths Advanced NSW Y11 Maths Extension 1

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Functions Polynomials Inverse Trig Functions and Identities Rates of Change Permutations and Combinations

NSW Y11 Maths - Extension 1 Permutations and Combinations Permutations

Resources for Permutations

  • Questions

    28

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    Click Here
  • Video Tutorials

    1


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  • HSC Questions

    2

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Permutations 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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Videos

Videos relating to Permutations.

  • Permutations - Video - Permutations Made Easy- Counting Using Permutations

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Theory

A permutation is an ordered selection or arrangement of all or part of a set of objects.

Factorial notation

If we arrange 5 objects in order the number of permutations is \(5 \times 4 \times 3 \times 2 \times 1\). This can be written as 5! (which can be found on your calculator)

Note that 0! Is defined to be 1.

The number of permutations of \(n\) objects \(r\) at a time is written \({}^n{P_r}\).

For example: \({}^{{}^5}{P_3} = 5 \times 4 \times 3 = \dfrac{{5 \times 4 \times 3 \times 2 \times 1}}{{2 \times 1}}\)

In general: \({}^n{P_r} = \dfrac{{n!}}{{\left( {n - r} \right)!}} \to {}^5{P_3} = \dfrac{{5!}}{{\left( {5 - 3} \right)!}}\) (\({}^n{P_r}\) is also on your calculator)