A-LevelMathematicsProbability and statistics9709/51 · May/June 2020 · Q44 Marks

In a music competition, there are 8 pianists, 4 guitarists and 6 violinists. 7 of these musicians will be selected to go through to the final. How many different selections of 7 finalists can be made if there must be at least 2 pianists, at least 1 guitarist and more violinists than guitarists?

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[1] Scenarios: 2P 3V 2G 8C2×6C3×4C2 = 28 × 20 × 6 = 3360; 2P 4V 1G 8C2×6C4×4C1 = 28 × 15 × 4 = 1680; 3P 3V 1G 8C3×6C3×4C1 = 56 × 20 × 4 = 4480; 4P 2V 1G 8C4×6C2×4C1 = 70 × 15 × 4 = 4200 (M1 for nCr × nCr × nCr with ∑r = 7)
[1] Two unsimplified products correct
[1] Summing the number of ways for 3 or 4 correct scenarios
[1] Total: 13 720

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2020 Paper 5 Variant 1, question 4.

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