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Six people are going to sit in a row on a bench. Romeo wasnts to sit next to Juliet. Caesar does not want to sit next to Brutus. Homer and Pierre can sit anywhere. In how many ways can these people be seated?

  • Math - ,

    1. Romeo, Juliet, _ _ _ _
    2. Juliet, Romeo, _ _ _ _
    3. _ Romeo, Juliet _ _ _
    4. _ Juliet, Romeo _ _ _
    5. _ _ Romeo, Juliet _ _
    6. _ _ Juliet, Romeo _ _
    7. _ _ _ Romeo, Juliet _
    8. _ _ _ Juliet, Romeo _
    9. _ _ _ _ Romeo, Juliet
    10._ _ _ _ Juliet, Romeo


    There are 5*2 possibilities for Romeo and Juliet.

    If we have a remaining seats with 4 in a row, (numbers 1, 2, 9 and 10 for Romeo and Juliet=4 possibilites for Romeo and Juliet), we can fill the rest

    Caesar _ Brutus _
    Brutus _ Caesar _
    Caesar _ _ Brutus
    Brutus _ _ Caesar

    Each of these has two possibilities for homer and Pierre, so there are 4*4*2 = 32 possibilities for everyone when Brutus, homer, Pierre and Caesar sit 4 in a row

    If three of Homer, Pierre, Brutus, and Caesar sit next to each other (numbers
    3, 4, 7, 8 for Romeo and Juliet = 4 possibilities for Romeo and Juliet), we have

    Caesar, Rom, Juliet, Brutus _ _
    Caesar, Rom, Juliet, _ Brutus _
    Caesar, Rom, Juliet, _ _ Brutus
    Brutus, Rom, Juliet, Caesar _ _
    Brutus, Rom, Juliet, _ Caesar _
    Brutus, Rom, Juliet, _ _ Caesar
    _ Rom, Juliet, Caesar _ Brutus
    _ Rom, Juliet, Brutus _ Caesar

    For each of these, there are 2 possibilites for Homer and Pierre
    8*4*2 = 48 for these arrangements

    For arrangements 5 and 6 for Romeo and Juliet, we have

    Caesar _ Rom, Juliet, _ Brutus
    Caesar _ Rom, Juliet, Brutus _
    Brutus _ Rom, Juliet, Caesar
    Brutus _ Rom, Juliet, _ Caesar

    4*2*2 = 16 possibilities

    Total # of possibilities is 16 + 32 + 48 = 96

    I hope I did this right!!

  • Math - ,

    2-39=

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