Find the number of different ways in which all 9 letters of the word MINCEMEAT can be arranged in each of the following cases. (A, E, I are vowels)

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [B1] Must see 90720
2. [B1] 5! seen multiplied (arrangement of consonants allowing repeats)
3. [B1] ⁶P₄ oe (i.e. 6 × 5 × 4 × 3, ⁶C₄ × 4!) seen mult (allowing repeats) no extra terms
4. [B1] Dividing by at least one 2! (removing at least one set of repeats)
5. [B1] Correct final answer
6. [M1] ⁵Cₓ or ⁷Pₓ seen alone, x = 2 or 3
7. [A1] Correct final answer not from ⁷C₂
8. [M1] Considering two scenarios of MME or EEM or MMEE with attempt, may be probs or perms
9. [M1] Summing three appropriate scenarios from the four need ⁵Cₓ seen in all of them
10. [A1] Correct final answer
11. [M1] ⁷Cₓ only seen, no other terms
12. [M1] ⁷C₃ only seen, no other terms
13. [A1] Correct final answer