0606/12 Oct/Nov 2025, Question 11: Combinations: Counting Selections
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
Solve the equation (n − 4) × ⁿ⁺¹C₅ = ⁿ⁺²C₇ for n, using combinations.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1(n − 4)(n + 1)!/((n − 4)! 5!) = (n + 2)!/((n − 5)! 7!)
- 2(n − 4)/(n − 4)! = 1/(n − 5)!, so (n + 1)!/5! = (n + 2)!/7!
- 37!/5! = (n + 2)!/(n + 1)! ⇒ 7 × 6 = n + 2
- 4n = 40
Answern = 40
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