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Math Help - Combinations

  1. #1
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    Combinations

    How many solutions are there to x_1+x_2+x_3+x_4=25 where x_n are all non-negative and x_1 is at most 5?
    Not sure where to start

    could u replace x_4 as x_4'+10 to get x_1+x_2+x_3+x_4'=20

    Then get... 23C3 from combinations formula for repetition is not allowed and order is irrelevant
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  2. #2
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    Quote Originally Posted by qwerty10 View Post
    How many solutions are there to x_1+x_2+x_3+x_4=25 where x_n are all non-negative and x_1 is at most 5?
    There are \dbinom{19+4-1}{19} solutions in which x_1\ge6.
    So now what do we do?
    Last edited by Plato; April 5th 2011 at 11:43 AM.
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  3. #3
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    would u get: 25+4-1C4-1 - 19+4-1C4-1?
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  4. #4
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    Quote Originally Posted by qwerty10 View Post
    would u get: 25+4-1C4-1 - 19+4-1C4-1?
    Yes you would. Note I changed the 5 to a 4 in my OP.
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