Find the number of different arrangements of the 9 letters in the word ANDROMEDA in which no consonant is next to another consonant. (The letters D, M, N and R are consonants and the letters A, E and O are not consonants.)

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [M1] 5! x 4! / e. e a positive integer, 1 can be implied. No other terms on numerator. No addition etc.
2. [M1] f / (2! x g!). f a positive integer, g = 1, 2. No other terms on denominator.
3. [A1] 720.
4. [B1] 7! / 2! - 6!. e, P_s - e, e a positive integer or 0.
5. [M1] 6! / d!, d! > 720, r = 1, 2.
6. [A1] 1800.
7. [M1] At least one correct unsimplified expression for an identified scenario.
8. [A1] [Total = ] 40 + 10 or 50 soi. If M0 scored, SC B1 [total =]50 www.
9. [B1] [Total number of selections =] 9C4 [= 126]. Accept evaluated, accept as denominator of probability expression. Do not condone C5 unless there is a clear explanation for selecting the letters not in the group.
10. [B1 FT] 0.396825... to at least 3SF. FT their attempted 40+10 / 126. Numerator must be from an attempt to find the 2 appropriate scenarios and must be evaluated.