◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2012 · Q55 Marks

A 4-digit number is formed by using four of the six digits 2, 3, 4, 5, 6 and 8; no digit may be used more than once in any number. How many different 4-digit numbers can be formed if

  1. (i)there are no restrictions,[2]
  2. (ii)the number is even and more than 6000?[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [M1] Evidence of 6, 5, 4, and 3 only
  2. [A1] 360
  3. [B1] Evidence of 2 × 3 for outside digits
  4. [B1] Evidence of 4 × 3 for inside digits
  5. [B1] 72

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Permutations and combinations, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2012 Paper 2 Variant 2, question 5.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Additional Mathematics questions

Permutations and combinationsMay/June 201510m

(a) A security code is to be chosen using 6 of the following: • the letters A, B and C • the numbers 2, 3 and 5 • the…

Permutations and combinationsMay/June 20158m

There are twenty numbered balls in a bag. Two of the balls are numbered 0, six are numbered 1, five are numbered 2 an…

Permutations and combinationsMay/June 20156m

In the expansion of (1 + 2x)ⁿ, the coefficient of x⁴ is ten times the coefficient of x². Find the value of the positi…

Differentiation and integrationMay/June 20149m

A solid circular cylinder has a base radius of r cm and a volume of 4000 cm³.

Vectors in two dimensionsMay/June 201410m

In this question \mathbf{i} is a unit vector due East and \mathbf{j} is a unit vector due North. At 12 00 hours, a sh…

TrigonometryMay/June 201411m

Solve tan²x + 5 tan x = 0 for 0circ ≤ x ≤ 180circ.

← Browse all past-paper questions

© 2026 Oracle Prep