Find the total number of different arrangements of the 8 letters in the word TOMORROW.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. M1 8! / (k! m!), k=1 or 2, m=1 or 3, not k=m=1 no additional terms
2. A1
3. M1 6! / k! – m, 1 ≤ k ≤ 3, m an integer, condone 2×(6!/k!)–m.
4. M1 w – 4! or w – 24, w an integer Condone w – 2 × 4!
5. A1
6. M1 ⁴C₃ × 3! + r or 4× 3! + r or ⁴P₃ × 3! + r, r an integer. Condone 2 × ⁴C₃ × 3! + r. 2 × 4× 3! + r or 2 × ⁴P₃ × 3! + r.
7. M1 q + ⁴C₂ × 3! × k or q + ⁴P₂ × 3! × k, k = 1,2, q an integer
8. A1
9. B1 Outcomes for 2 identifiable scenarios correct, accept unsimplified.
10. M1 Add 4 or 5 identified correct scenarios only values, no additional incorrect scenarios, no repeated scenarios, accept unsimplified, condone use of permutations.
11. A1 All correct and added
12. M1 their '50' / ⁸C₄ , accept numerator unevaluated.
13. A1
14. B1 Outcomes for 5 identifiable scenarios correct, accept unsimplified.
15. M1 Add 9, 10 or 11 identified correct scenarios only values, no additional incorrect scenarios, no repeated scenarios, accept unsimplified, condone use of permutations.
16. A1 All correct and added
17. M1 their '50' / ⁸C₄, accept numerator unevaluated.
18. A1