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Persons sitting in a row

  1. Mar 26, 2014 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    The number of ways in which 4 persons P1,P2,P3,P4 can be arranged in a row such that P2 does not follow P1, P3 does not follow P2 and P4 does not follow P3 is


    3. The attempt at a solution

    Let us assume that P1 occupies the first position. So, the next position can be occupied by P3 or P4. Thus, there are 2 ways by which the required arrangement can be made, P1 occupying the first seat. Since there are 4 persons, we have 2*4=8 ways by which the persons can be seated according to the given condition. But this is not correct. I can't figure out where I'm going wrong.
     
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  3. Mar 26, 2014 #2

    LCKurtz

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    What does it mean for one person to "not follow" another when they are seated in a row?
     
  4. Mar 27, 2014 #3

    utkarshakash

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    I'm assuming that they should not be seated next to each other.
     
  5. Mar 27, 2014 #4

    haruspex

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    I would interpret it as meaning they are not adjacent in a specific order. I.e. if we regard the leftmost position as the first position then P2 cannot be immediately to the right of P1, etc. P2-P1-P4-P3 would be valid.
    This means you cannot assume P1 is in first position.
    The only other interpretation of those words that seems reasonable to me is that P2 cannot be anywhere to the right of P1, etc. But then the problem becomes trivial.
     
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