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Achievement objective M8-3

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • use permutations and combinations.


  • Understands the basic terms and notation of permutations and combinations, including:
    n P r equals n factorial divided by bracket n minus r bracket factorial. , n C r equals n factorial divided by bracket n minus r bracket factorial divided by r factorial.
  • Selects and uses appropriate methods to find numbers of distinct arrangements or selections from a given number of objects in order to solve problems and calculate probabilities, including:
    • the multiplication principle
    • factorials
    • permutations, including fixed position of items, groups of items, and identical items
    • combinations including restrictions on the selections and selecting from more than one group.
  • See key mathematical ideas on NZmaths.


M8-3 links from M7-3.

Possible context elaborations

  • Straightforward applications such as choosing a sample of 3 girls and 4 boys from a class of 16 girls and 12 boys.
  • Calculate probabilities of winning the different Lotto divisions.
  • Cases where repetition is permissible such as selecting the three letters for New Zealand vehicle number plates.
  • Possible investigations include Pascal’s triangle.
  • Opportunities for proof, for example, show nC + nC(n-r) = (n + 1) C.

Assessment for qualifications

NCEA achievement standards at levels 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The NZQA subject-specific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.

Learn more:

The following achievement standard(s) could assess learning outcomes from this AO:

  • There are currently no achievement standards that could assess learning outcomes from this AO.

Refer to the mathematics and statistics matrix.

Last updated September 26, 2013