O-LevelAdditional MathematicsPermutations and combinations4037/12 · Oct/Nov 2015 · Q47 Marks

6 books are to be chosen from 8 different books.

(a)(i)Find the number of different selections of 6 books that could be made.[1]
(a)(ii)A clock is to be displayed on a shelf with 3 of the 8 different books on each side of it. Find the number of ways this can be done if there are no restrictions on the choice of books,[1]
(a)(iii)3 of the 8 books are music books which have to be kept together.[2]
(b)A team of 6 tennis players is to be chosen from 10 tennis players consisting of 7 men and 3 women. Find the number of different teams that could be chosen if the team must include at least 1 woman.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[B1] 28
[B1] 20160
[B1] for realising that the music books can be arranged amongst themselves and consideration of the other 5 books
[B1] for the realisation that the above arrangement can be either side of the clock.
[B1, B1] B1 for 10C6, B1 for 7C6
[B1] (final result for part b)

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Topic: Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2015 Paper 1 Variant 2, question 4.

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