A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2024 · Q56 Marks

In a class of 21 students, there are 10 violinists, 6 guitarists and 5 pianists. A group of 7 is to be chosen from these 21 students. The group will consist of 4 violinists, 2 guitarists and 1 pianist.

(a)In how many ways can the group of 7 be chosen?[2]
(b)On another occasion a group of 5 will be chosen from the 21 students. The group must contain at least 2 violinists, at least 1 guitarist and at most 1 pianist.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[M1] ¹⁰Cₐ × ⁶Cₓ × ⁵Cᵧ, a + b + c = 7, a,b,c integers. No other terms present but condone × 6 or × 3!.
[A1]
[M1] One product using 2 or 3 combinations with upper numbers correct and lower numbers summing to 5 and linked to a correct identified scenario. Condone the consistent use of permutations.
[B1] 2 identified outcomes evaluated accurately, accept unsimplified.
[M1] Add values of 5 correct scenarios, no incorrect/repeated scenarios.
[A1] If either or both Ms not awarded, SC B1 for 10935 WWW

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2024 Paper 5 Variant 2, question 5.

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