A 4-digit code is to be formed using 4 different numbers selected from 2, 3, 4, 5, 6, 7, 8 and 9. Find how many possible codes there are if the code forms

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [M2] e.g. [starts with 5, 7, 9 and ends in 3 or two of 5, 7, 9] 3 × 6 × 5 × 3 or 270
2. [M2] and [starts with 6, 8 and ends in 3,5,7, 9] 2 × 6 × 5 × 4 or 240
3. [M2] OR [ends with 3 and starts with 5, 6, 7, 8, 9] 5 × 6 × 5 × 1 or 150
4. [M2] and [ends with 5, 7, 9 and starts with 6, 8 or two of 5, 7, 9] 4 × 6 × 5 × 3 or 360
5. [M1] for a partially correct method equivalent to one of the above two steps
6. [A1] 510
7. [M2] e.g. [starts with 5, 7 and ends with 2, 3 and 5 or 7] 2 × 6 × 5 × 3 = 180
8. [M2] and [starts with 6, 8, 9 and ends with 2, 3, 5, 7] 3 × 6 × 5 × 4 = 360
9. [M2] OR [ends with 2, 3 and starts with 5, 6, 7, 8, 9] 5 × 6 × 5 × 2 or 300
10. [M2] and [ends with 5, 7 and starts with 6, 8, 9 and 5 or 7] 2 × 6 × 5 × 4 or 240
11. [M1] for a partially correct method equivalent to one of the above two steps
12. [A1] 540