O-LevelAdditional MathematicsPermutations and combinations4037/11 · May/June 2025 · Q124 Marks
In this question n ≥ 6.
- Use an algebraic method to show that ⁿC₅ - ⁿ⁻¹C₅ can be written as ⁿ⁻¹C₄.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [M1] For substituting ⁿC₅ and ⁿ⁻¹C₅
- [M1] dep on previous M1 awarded; For Factorising (n-1)!/(n-6)!5! or (n-1)!/(n-5)!5!
- [M1] dep on at least one previous M1 awarded; Simplifying fraction (n-1)!/(n-6)!5! × [5/(n-5)] oe
- [A1] Completes argument: (n-1)!/(n-6)!5! × [5/(n-5)] = (n-1)!/(n-5)!4! = ⁿ⁻¹C₄
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →