How many different 5-digit numbers can be formed using the digits 1, 2, 4, 5, 7 and 9 if no digit is repeated?

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

1. [B1] (a)(i) 720
2. [B1] (a)(ii) 240
3. [B1] (a)(iii) Starts with either a 2 or a 4: 48 ways
4. [B1] (a)(iii) Does not start with either a 2 or a 4: 96 ways (i.e. starts with 1 or 5)
5. [B1] (a)(iii) Total = 144
6. [B1] (a)(iii) Ends with a 2, starts with a 1,4 or 5 : 72 ways
7. [B1] (a)(iii) Ends with a 4, starts with a 1,2 or 5 : 72 ways
8. [B1] (a)(iii) Total =144
9. [B2] (a)(iii) B2 for correct expression seen, allow P notation
10. [B1] (a)(iii) Allow P notation here, for B2
11. [B1] (b) With twins: ⁱ⁶C₄ (=1820)
12. [B1] (b) Without twins: ⁱ⁶C₆ (= 8008)
13. [B1] (b) Total: 9828
14. [B1,B1] (b) B1 for ⁱ⁸C₆ -....,, B1 for 2×ⁱ⁶C₅
15. [B1] (b) = 9828