0606/12 May/Jun 2026, Question 13: Combinations: Counting Selections
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Prove that the difference between the combinations n+2 choose 3 and n choose 3 equals n² for every n ≥ 3.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1ⁿ⁺²C₃ − ⁿC₃ = (n + 2)!/((n − 1)! 3!) − n!/((n − 3)! 3!)
- 2= (n + 2)(n + 1)n/6 − n(n − 1)(n − 2)/6
- 3= (n/6)(n² + 3n + 2 − (n² − 3n + 2))
- 4= (n/6)(6n) = n²
Answerⁿ⁺²C₃ − ⁿC₃ = n² shown
Stuck on a step? Read the free lesson: Combinations: Counting Selections
Practise more combinations: counting selections questions
Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on combinations: counting selections
Also searched as: 0606/12/M/J/26 · 0606_s26_qp_12 · 0606 s26 12 · question 13.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.