Five students tried this IB exam question; They could not agree on the answer.

Mr Blue, Mr Black, Mr Green, Mrs White, Mrs Yellow and Mrs Red sit around a circular table for a meeting. Mr Black and Mrs White must not sit together. Calculate the number of different ways these six people can sit at the table without Mr Black and Mrs White sitting together.

Student A thought the answer was 672, Students B and D 72 and Student C, 432.

(1) Use this simulation to generate the experimental probabilities to help you figure who (if anyone) was correct.

(2) Prove the answer, showing your method clearly.

(3) TOK Assignment - Comment the strengths and weaknesses of the type of "proof" offered by this simulation. Keywords - Validity, Inductive, Deductive, Infinity, Rigorous, Subjective, Necessary, Sufficient.

(4) How could you use the experimental probabilities to adapt the sheet to give a predicted number that answers the question?