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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.

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.

Last updated September 14, 2018