Recognising permutations vs combinations

Sample Recognising permutations vs combinations questions

A few of the 3 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 12 marksGrade 7
   A school is selecting 3 students from a class of 12 to represent the school at a debate competition. All three selected students have the same role. State whether the number of ways to select the students is a permutation or a combination, giving a reason. [2]
   Show the worked solution

   The three selected students all have the same role (representing the school) - there's no distinction between who is "first", "second", or "third".

   Since the order of selection doesn't matter, this is a combination.
2. Question 22 marksGrade 7
   From 6 candidates, a chairperson and a secretary are to be selected - these are two different roles. State whether the number of ways to select the chairperson and secretary is a permutation or a combination, giving a reason. [2]
   Show the worked solution

   Chairperson and secretary are two distinct roles, so assigning candidate A to chairperson and B to secretary is a DIFFERENT outcome from assigning B to chairperson and A to secretary.

   Since the order (which role each candidate gets) matters, this is a permutation.

What are the common mistakes in Recognising permutations vs combinations?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Assumes a selection of a fixed number of items is always a permutation, without checking whether the items/roles involved actually have distinguishable order or position

  Whether the order of choosing matters depends on the ROLES involved, not the number of items chosen - the 5 team members in (a) all have the same status, so their selection is a combination, while the 5 books in (b) occupy distinct positions in a row, so their arrangement is a permutation.

• Treats a selection as a permutation regardless of whether the selected items have distinct roles, instead of checking whether order/role actually matters

  Whether a selection is a permutation or a combination depends on whether the ORDER (or distinct roles) matters - here, the three students all have the SAME role, so selecting {A, B, C} is identical to selecting {B, A, C}, making this a combination, not a permutation.

• Treats two distinct roles or positions as interchangeable, missing that order/assignment matters, making the scenario a permutation rather than a combination

  Chairperson and secretary are DIFFERENT roles - choosing candidate A as chairperson and B as secretary is a different outcome from choosing B as chairperson and A as secretary, so the order (which role each person gets) matters, making this a permutation.

Quick answers about Recognising permutations vs combinations

How many Recognising permutations vs combinations practice questions are there?

There are 3 self-marking Additional Maths Maths questions on Recognising permutations vs combinations, written for Cambridge IGCSE Additional Maths (0606) across Single tier. Each one is marked instantly and has a full worked solution.

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