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O-LevelAdditional MathematicsPermutations and combinations4037/21 · May/June 2024 · Q58 Marks

There are 3 women, 2 men and 4 children in a choir.

  1. (a)(i)Find the number of possible arrangements if the first person and last person are both women.[2]
  2. (a)(ii)Find the number of possible arrangements if all the children stand next to each other.[2]
  3. (b)(i)Find the number of different selections if no man is chosen.[2]
  4. (b)(ii)Find the number of different selections if at least 2 women are chosen.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [M1] for 3 × 7! × 2 or ³P₂ × ⁷P₇ oe
  2. [A1] 30 240
  3. [M1] for 4! × 6! oe or ⁴P₄ × ⁶P₆ oe
  4. [A1] 17 280
  5. [M1] for ⁷C₄
  6. [A1] 35
  7. [M1] for ³C₂ × ⁶C₂ + ³C₃ × ⁶C₁ oe
  8. [A1] 51

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About this question

Topic
Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2024 Paper 2 Variant 1, question 5.

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