Permutations and combinations: past paper questions
Real questions on permutations and combinations
The newest 20 of 83 written questions. Open one to see it on the real paper.
- 4037/12 · October/November 2025 · Q11[3]
3-mark “Solve” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/22 · October/November 2025 · Q5b[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/22 · October/November 2025 · Q5c[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/23 · October/November 2025 · Q5b[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/23 · October/November 2025 · Q5c[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/11 · May/June 2025 · Q12[4]
4-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/21 · May/June 2025 · Q3a[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/21 · May/June 2025 · Q3b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/22 · May/June 2025 · Q5a(i)[1]
1-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/22 · May/June 2025 · Q5a(ii)[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/22 · May/June 2025 · Q5a(iii)[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/22 · October/November 2024 · Q7a(ii)[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/22 · October/November 2024 · Q7a(iii)[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/22 · October/November 2024 · Q7b[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/23 · October/November 2024 · Q11a(i)[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/23 · October/November 2024 · Q11a(ii)[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/23 · October/November 2024 · Q11b[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/12 · May/June 2024 · Q4a[1]
1-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/12 · May/June 2024 · Q4b[1]
1-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 4037/12 · May/June 2024 · Q4c[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
Fewer candidates were able to obtain the number of 6-digit numbers divisible by 5. This was because some candidates incorrectly thought that a 6-digit number could start with 0 when dealing with their solutions. This highlights the importance of reading the information in the stem of the question carefully.
— Examiner report, October/November 2023, 4037/12 Q7(a)(ii) (Cambridge)
Fewer candidates were able to obtain the correct answer of 18. If all 6 doctors are on the committee then there is only one place left to fill. This can be filled by any one of the 10 nurses or 8 dentists.
— Examiner report, October/November 2023, 4037/12 Q7(b)(ii) (Cambridge)
The most straightforward solution was to consider the number of committees that could be formed if there were no dentists and subtract this from the answer to part (i), the total number of committees. This method was used by many of those that attempted this part of the question. Others chose a longer method by listing all the 7 possible combinations with no dentists on the committee. This method...
— Examiner report, October/November 2023, 4037/12 Q7(b)(iii) (Cambridge)
Past papers, syllabus and examiner reports © UCLES (Cambridge University Press & Assessment). Questions are matched to topics from the official syllabus. AssessPro is independent and not endorsed by Cambridge.