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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 Combinations

Resources for Combinations

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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/

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  • Combinations - Video - Combinations made easy

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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.