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Another question on permutations

  1. Aug 4, 2013 #1
    1. The problem statement, all variables and given/known data
    8. Using the digits 1, 2, 3, 5, 7, 8 how many 4 digit numbers greater than 5,364 could be constructed if:
    a) Repetition of the digits is allowed?
    b) Repetition of the digits is not allowed?


    2. Relevant equations



    3. The attempt at a solution
    for part a:
    2*6*6*6 (for 8 and 7 as the first digit)
    +
    1*4*2*3 (for 5 as the first digit)

    But it is incorrect :(

    Correct answer is 552 for part a and 150 for part b
     
    Last edited: Aug 4, 2013
  2. jcsd
  3. Aug 4, 2013 #2

    CAF123

    User Avatar
    Gold Member

    For part a), consider 3 cases: The first digit > 5, the first two digits being 5 and 3, the first digit being 5.

    If the first digit is 5 and the second 3, then this puts a restriction on the last two. If the first digit is 5 and the second > 3, then there is no restriction on the last two. This is what your answer does not take into consideration.
     
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