The 9 letters in the word HAPPINESS are divided at random into a group of 5 and a group of 4.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

1. [B1]
2. [M1] a – 7!/2! × b a= their 6(a) or correct, b = 1,2.
3. [M1] a – 7!/c! × 2 a = their 6(a) or correct, c = 1,2.
4. [A1 FT] ft their 6(a) – 5040.
5. [M1] Finding correct number of ways for one of these correctly identified scenarios.
6. [M1] Adding no of ways for 3 correctly identified scenarios.
7. [A1]
8. [M1] Finding correct number of ways for one of these correctly identified scenarios.
9. [M1] Adding no of ways for 3 correctly identified scenarios.
10. [A1]
11. [M1] Identifying no of ways if S^^S is in position 1 or 6.
12. [M1] Identifying no of ways if S^^S is in position 2, 3, 4 or 5.
13. [M1] Adding no of ways for 6 scenarios (or 26 × 5!).
14. [A1] SC B1 for 3120 if any method marks are withheld.
15. [M1] a×⁵C₂, a×⁵C₃, or ⁵C₂+⁵C₃ seen as a numerator of one or two fractions where a is 1 or 2, no extra terms.
16. [M1] ⁹C₅ or ⁹C₄ seen (no addition, multiplication) as a denominator of one or two fractions.
17. [A1]
18. [M1] a×5×4×4×3 seen as a numerator of a fraction. where a = 1 or 2.
19. [M1] 9×8×7×6 seen as a denominator of a fraction.
20. [A1]