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O-LevelAdditional MathematicsPermutations and combinations4037/12 · May/June 2013 · Q25 Marks

A 4-digit number is to be formed from the digits 1, 2, 5, 7, 8 and 9. Each digit may only be used once. Find the number of different 4-digit numbers that can be formed if

  1. (i)there are no restrictions,[1]
  2. (ii)the 4-digit numbers are divisible by 5,[2]
  3. (iii)the 4-digit numbers are divisible by 5 and are greater than 7000.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

  1. [1] 6 × 5 × 4 × 3 = 360 or ⁶P₄ = 360 B1 unsimplified/evaluated
  2. [1] M1 for a correct attempt unsimplified
  3. [1] Number of 4 digit numbers = 60 A1
  4. [1] M1 for a correct attempt unsimplified
  5. [1] Number of 4 digit numbers = 36 A1

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About this question

Topic
Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2013 Paper 1 Variant 2, question 2.

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