A-LevelMathematicsProbability and statistics9709/51 · May/June 2025 · Q57 Marks

In a group of 20 musicians, there are 9 guitarists, 6 pianists and 5 drummers. 6 musicians are selected from these 20 to perform at a concert.

(a)Find the number of different ways in which the 6 musicians can be selected if there must be at least 3 guitarists, at most 2 pianists and exactly 1 drummer.[4]
(b)Three bands will be selected from the original group of 20 musicians. Each band will consist of 3 guitarists, 1 pianist and 1 drummer. No musician can be in more than one band. The first band selected will play at a concert in France, the second band selected will play in Italy and the third band selected will play in Spain.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[B1] Correct outcome/value for either the 1st or 2nd scenario clearly identified, accept un-simplified, WWW.
[M1] 2 correct outcomes/values obtained, accept un-simplified
[M1] Sum of 3 correct scenarios, may be identified by un-simplified expression.
[A1] CAO If one or both M marks not awarded, SCB1 for 10710 WWW.
[M1] ⁹C3 x ⁶C1 x ⁵C1 or ⁶C3 x ⁵C1 x ⁴C1 seen, condone x 3 or x3!.
[M1] their 2520 x their 400 x their 12 seen, accept un-simplified, condone x 3 or x3!.
[A1] Condone 12100000. If one or both M marks not awarded, SCB1 for 12096000 (CAO) WWW.

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