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O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2017 · Q57 Marks

Naomi is going on holiday and intends to read 4 books during her time away. She selects these books from 5 mystery, 3 crime and 2 romance books. Find the number of ways in which she can make her selection in each of the following cases.

  1. (i)There are no restrictions.[1]
  2. (ii)She selects at least 2 mystery books.[3]
  3. (iii)She selects at least 1 book of each type.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [B1] 10C4 = 210
  2. [B3] 2 Mystery 2 others = 5C2 × 5C2 =100; B1 for one combination, unsimplifiied
  3. 3 Mystery 1 other = 5C3 × 5C1 = 50; B1 for second combination, unsimplifiied
  4. 4 Mystery = 5C4 =5; B1 for third combination, unsimplifiied and total
  5. Total 155
  6. [B3] 2M1C1R = 5C2 × 3C1 x 2C1 = 60; B1 for one combination, unsimplifiied
  7. 1M2C1R = 5C1 × 3C2 x 2C1 = 30; B1 for second combination, unsimplifiied
  8. 1M1C2R = 5C1 × 3C1 x 2C2 =15; B1 for third combination, unsimplifiied and total
  9. Total 105

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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, Oct/Nov 2017 Paper 2 Variant 2, question 5.

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