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O-LevelAdditional MathematicsPermutations and combinations4037/21 · Oct/Nov 2010 · Q66 Marks

A 4-digit number is formed by using four of the seven digits 1, 3, 4, 5, 7, 8 and 9. No digit can be used more than once in any one number. Find how many different 4-digit numbers can be formed if

  1. (i)there are no restrictions,[2]
  2. (ii)the number is less than 4000,[2]
  3. (iii)the number is even and less than 4000.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.

  1. [B1] (i) 7 × 6 × 5 × 4
  2. [B1] (i) 840
  3. [M1] (ii) 2 × 6 × 5 × 4 or ²⁄₇ × (840)
  4. [A1] (ii) 240
  5. [M1] (iii) 2 × 5 × 4 × 2 or ²⁄₆ × (240) or clear indication of method
  6. [A1] (iii) 80

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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 2010 Paper 2 Variant 1, question 6.

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