O-LevelAdditional MathematicsPermutations and combinations4037/11 · May/June 2023 · Q77 Marks
7 (a) A team of 8 people is to be chosen from a group of 15 people.
- (a)(i)Find the number of different teams that can be chosen.[1]
- (a)(ii)Find the number of different teams that can be chosen if the group of 15 people contains a family of 4 people who must be kept together.[3]
- (b)Given that (n+9) × ⁿP₁₀ = (n²+243) × ⁿ⁻¹P₉, find the value of n.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [1] B1 Must be evaluated not just 15C8
- [3] B1 Must be evaluated not just 11C4 or implied by a correct answer
- B1 Must be evaluated not just 11C8 or implied by a correct answer
- B1 Total: 495
- [3] B1 for either nP10 = n!/(n-10)! or n-1P9 = (n-1)!/(n-1-9)! = (n-1)!/(n-10)!
- B1 dep for n(n+9) = n²+243
- B1 n = 27
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