How many different arrangements are there of the 10 letters in the word REGENERATE?

Mark scheme

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

1. [B1] [10! / (2!4!)] = 75600
2. [M1] 4! SOI in all terms leading to final answer. Allow 24 if 4! = 24 is seen.
3. [M1] Ignoring any values used to justify 4!. Either 3! SOI in expression leading to final answer, or at least 6 distinct scenarios identified and added in expression leading to final answer. Condone 3 distinct scenarios × 2. Ignore repeated scenarios.
4. [A1] 4! × 3! Fully correct unsimplified expression leading to final answer.
5. [B1] WWW
6. [B1] 5!/2! seen (arrangements of consonants).
7. [B1] 5!/4! seen (arrangements of vowels).
8. [M1] 5!/r! × 5!/s! × 2, r = 1 or 2, s = 1, 4, 4! or 24.
9. [M1] their 600 / their (a) or their 600 / 75600
10. [A1] Accept 600/75600 OE.
11. [(B1)] 5! seen (arrangements of consonants).
12. [(B1)] A second 5! seen (arrangements of vowels).
13. [(M1)] 5! × 5! × k, k = 1 or 2.
14. [(M1)] their 28800 / 10!
15. [(A1)] Accept 600/75600 OE.
16. [(B1)] 5/10 × 4/9 × 3/8 × 2/7 × 1/6 seen.
17. [(B1)] A second 5/10 × 4/9 × 3/8 × 2/7 × 1/6 seen.
18. [(M1)] 5/10 × 4/9 × ... × k.
19. [(M1)] their 5×4×3×2×1×5×4×3×2×1 / 10×9×8×7×6×5×4×3×2×1
20. [(A1)] Accept 28800/362800 OE.