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Math Help - Easy combinatorics problem

  1. #1
    MHF Contributor alexmahone's Avatar
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    Easy combinatorics problem

    How many four-digit positive integers are there that contain the digit 1?
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  2. #2
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    Re: Easy combinatorics problem

    Quote Originally Posted by alexmahone View Post
    How many four-digit positive integers are there that contain the digit 1?
    To be clear 0109=109 is not a four digit number, right??
    There are 9\cdot 10^3 four-digit numbers.
    Of those there are 8\cdot 9^3 that do not contain any 1's.

    So how many contain at least one 1?
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  3. #3
    Member anonimnystefy's Avatar
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    Re: Easy combinatorics problem

    hi alexmahone

    should the digits be the same or must be different?
    if they are the same then there are:
    1000+900+900+900=2800

    if they are not the same then there are:
    720+648+648+648=2664
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