The 9 letters in the word CROCODILE are: C (2), R (1), O (2), D (1), I (1), L (1), E (1).

Mark scheme

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

1. B1 [9!/(2!2!) =] 90 720
2. M1 w!/2! - y, w = 6, 7 y an integer. Condone 2 x w!/2! - y.
3. M1 a - 6! or a – 720, a an integer resulting in a positive answer.
4. A1 [1800]
5. M1 5! x b, b integer >1.
6. M1 cx (6x5)/2! or 6C2 or 15), c integer > 1.
7. A1 [1800]
8. B1 Correct outcome/value for 1 identified scenario. Accept unsimplified. WWW [CCO = 5C1 = 5] [CC_ = 5C2 = 10] [OOC = 5C1 = 5] [OO_ = 5C2 = 10] [C_ _ = 5C3 = 10] [O_ _ = 5C3 = 10]
9. M1 Add 5 or 6 values of appropriate scenarios only, no additional incorrect scenarios, no repeated scenarios. Accept unsimplified. Condone use of permutations.
10. A1 [Total =] 50
11. B1 A correct scenario calculated accurately. Accept unsimplified. [Both Os in group with a C: 5C2 = 10] [Both Os in group without a C: 5C2 × 3C2 = 30] [One O in a C group, one not: 5C1 × 4C2 = 30] [One O with each C: (5C1 × 4C1) ÷2! = 10]
12. M1 Add 3 or 4 correct scenario values, no incorrect scenarios, accept repeated scenarios. Accept unsimplified.
13. A1 [Total =] 80
14. B1 A correct scenario calculated accurately. Accept unsimplified. [CCO O^^ ^^^ = 5C2 = 10] [CC^ O^^ O^^ = 5C1 ×4C2 = 30] [CC^ OO^ ^^^ = 5C1 × 4C1 = 20]
15. M1 Total subtract 2 or 3 correct scenario values, no incorrect scenarios. Accept unsimplified.
16. A1 [Total =] 80