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A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2018 · Q46 Marks

Find the number of different ways that 5 boys and 6 girls can stand in a row if all the boys stand together and all the girls stand together.

  1. (i)Find the number of different ways that 5 boys and 6 girls can stand in a row if all the boys stand together and all the girls stand together.[3]
  2. (ii)Find the number of different ways that 5 boys and 6 girls can stand in a row if no boy stands next to another boy.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [B1] k×5! or m×6! (k,m integer, k,m ≥ 1), no inappropriate addition
  2. [B1] n × 5! × 6! (n integer, n ≥ 1), no inappropriate addition
  3. [B1] Correct final answer, isw rounding (www scores B3) All marks based on their final answer
  4. [M1] k× 6! or k × ⁷P₅ (k is an integer, k ≥ 1) no inappropriate add. (⁷P₅ = 7 × 6 × 5 × 4 × 3 or ⁷C₅ × 5!)
  5. [M1] Correct unsimplified expression
  6. [A1] Correct exact final answer (ignore subsequent rounding)

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2018 Paper 6 Variant 2, question 4.

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