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O-LevelAdditional MathematicsPermutations and combinations4037/11 · Oct/Nov 2011 · Q46 Marks

Six-digit numbers are to be formed using the digits 3, 4, 5, 6, 7 and 9. Each digit may only be used once in any number. Find how many of these six-digit numbers are

  1. (i)Find how many different six-digit numbers can be formed.[1]
  2. (ii)even,[1]
  3. (iii)greater than 500000,[1]
  4. (iv)even and greater than 500000.[3]

Mark scheme

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

  1. [1] (i) 6! = 720
  2. [1] (ii) 2 × 5! = 240
  3. [1] (iii) 4 × 5! = 480
  4. [1] (iv) Even first and last: 4! (24)
  5. [1] (iv) Odd first and even last: 4 x 4! (144)
  6. [1] (iv) Total: 7 x 4! = 168

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About this question

Topic
Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2011 Paper 1 Variant 1, question 4.

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