NSW Y11 Maths - Extension 1 Permutations and Combinations Identical Objects

Resources for Identical Objects

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Identical Objects 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 relating to Identical Objects.

  • Identical Objects - Video - Arranging Identical Objects

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Theory

The number of ways of arranging \(n\) objects in a row when \(p\) objects are identical and \(q\) objects are identical (but different to the others) is: \(\dfrac{{n!}}{{p!q!}}\).

For example: In how many ways can the word BANANA be arranged in a line?

\(n = 6,\,{\rm{A's}} = 3,\,{\rm{B's}} = 2\)

\(\dfrac{{n!}}{{p!q!}} = \dfrac{{6!}}{{3!2!}} = 60\)