Find the number of different arrangements of the 9 letters in the word ACTIVATED.

Mark scheme

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

1. [M1] h! / (2!xj!), h = 7, 8, 9; j = 1, 2
2. [A1]
3. [M1] (7!/2!) * k, k positive integer 1 < k < 7
4. [M1] Add their no of ways for 3 identified correct scenarios, no additional incorrect scenarios, accept unsimplified.
5. [A1]
6. [B1] Correct no of ways for 4 correctly identified scenarios, accept unsimplified.
7. [M1] Add no of ways for 5 or 6 identified correct scenarios, no additional incorrect scenarios, no repeated scenarios, accept unsimplified.
8. [A1] All correct and added
9. [M1] their 86 / 9C5 or their identified total accept numerator unevaluated
10. [A1]