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Homework Help: Simple understanding question

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Given a random permutation of integer in the set (1,2,3,4,5), let X equal the number of integer that are in their natural position.

    3. The attempt at a solution

    i don't understand "number of integer that are in their natural position"
    can someone explain it. please
  2. jcsd
  3. Feb 23, 2010 #2


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    It's the number of integers that are mapped to themselves under the random permutation.
  4. Feb 23, 2010 #3
    hmm still confused, im sorry for my bad english,

    let me tell what i understand,

    the universal set are

    (1,2,3,4,5),(5,4,3,2,1),(1,2,3,5,4) and so on,
    there's 5!=120 in total,

    so, which are integer that maps to itself? can give me some example.. :)
  5. Feb 23, 2010 #4
    If, for example, your permutation is (2,3,1,4,5) then X = 2 because 4 and 5 are in their original, or natural positions.
  6. Feb 23, 2010 #5
    OOOOOOOOOOOOOOOOOOOOOOOO, i get it, thankssss,
    thank you very much
  7. Feb 24, 2010 #6
    But what about 3 and 1
  8. Feb 24, 2010 #7
    he means, that, 4 and 5 is the integer in its natural position...
    so, x=2 which means, there are two integer in its natural position..

    (2,3,1,*,*) is not in their natural position because (1,2,3,*,*) is their actual position


    (5,2,3,4,1) , so 2,3, and 4 are in thier natural position, so x=3
  9. Feb 24, 2010 #8
    Thank, I got it.
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