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O-LevelAdditional MathematicsPermutations and combinations4037/12 · May/June 2017 · Q811 Marks

(a) A 5-digit number is to be formed from the seven digits 1, 2, 3, 5, 6, 8 and 9. Each digit can only be used once in any 5-digit number. Find the number of different 5-digit numbers that can be formed if (b) Ranjit has 25 friends of whom 15 are boys and 10 are girls. Ranjit wishes to hold a birthday party but can only invite 7 friends. Find the number of different ways these 7 friends can be selected if

  1. (a)(i)there are no restrictions,[1]
  2. (a)(ii)the number is divisible by 5,[1]
  3. (a)(iii)the number is greater than 60000,[1]
  4. (a)(iv)the number is greater than 60000 and even.[3]
  5. (b)(i)there are no restrictions,[1]
  6. (b)(ii)only 2 of the 7 friends are boys,[1]
  7. (b)(iii)the 25 friends include a boy and his sister who cannot be separated.[3]

Mark scheme

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

  1. [B1] 2520
  2. [B1] 360
  3. [B1] 1080
  4. [B1] 6 or 8 to start with
  5. [B1] 9 to start with
  6. [DB1] Dependent on both previous B marks Total number of ways = 420
  7. [B1] 480700
  8. [B1] 26460
  9. [B1] With brother and sister 23C5 = 33649
  10. [B1] Without brother and sister 23C7 = 245157
  11. [B1] for 23C5 + 23C7 and evaluation

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About this question

Topic
Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 11 marks.
Source
O-Level Additional Mathematics, May/June 2017 Paper 1 Variant 2, question 8.

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