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O-LevelAdditional MathematicsPermutations and combinations4037/21 · May/June 2011 · Q67 Marks

A shelf contains 8 different travel books, of which 5 are about Europe and 3 are about other regions.

  1. (a)(i)Find the number of different ways the books can be arranged if there are no restrictions.[2]
  2. (a)(ii)Find the number of different ways the books can be arranged if the 5 books about Europe are kept together.[2]
  3. (b)3 DVDs and 2 videotapes are to be selected from a collection of 7 DVDs and 5 videotapes. Calculate the number of different selections that could be made.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.

  1. [1] (a)(i) Evidence of 8, 7, 6, 5, 4, 3, 2, 1 or 8!
  2. [1] (a)(i) 40320
  3. [1] (a)(ii) Evidence of 5! (120) or 4! (or 24)
  4. [1] (a)(ii) 2880
  5. [1] (b) 7C3 (= 35) and 5C2 (= 10)
  6. [1] (b) Multiply
  7. [1] (b) 350

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About this question

Topic
Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2011 Paper 2 Variant 1, question 6.

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