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AMC 12 2017a Problem 14

  • Paper

Alice refuses to sit next to either Bob or Carla. Derek refuses to sit next to Eric. How many ways are there for the five of them to sit in a row of 55 chairs under these conditions?

\textbf{(A)}\ 12 \textbf{(B)}\ 16 \textbf{(C)}\ 28 \textbf{(D)}\ 32 \textbf{(E)}\ 40

Dataset text AMC 12 2000 to 2025. Quoted with source.

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C

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