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Math Help - Find the number of integer solutions

  1. #1
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    Find the number of integer solutions

    Find the number of integer solutions x1+x2+x3=20 with x1≥0 x2≥1 x3≥1
    is this C(20,2)?
    Thank you.
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  2. #2
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    Re: Find the number of integer solutions

    How did you get that result?

    Take y2 = x2 - 1 and y3 = x3 - 1

    Rephrase to x1 + (y2 + 1) + (y3 + 1) = 20 or x1 + y2 + y3 = 18

    And out pops C(18+2,2). I think you have it!
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  3. #3
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    Re: Find the number of integer solutions

    Quote Originally Posted by tinabaker View Post
    Find the number of integer solutions x1+x2+x3=20 with x1≥0 x2≥1 x3≥1
    is this C(20,2)?
    When posting please do not use special fonts.
    The number of way to put N 1's into K variables is \tbinom{N+K-1}{N}.
    If we want x_2\ge 1~\&~x_3\ge 1 we can think of putting a 1 into each of those two variables.
    So is the answer \tbinom{18+3-1}{18}~?
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  4. #4
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    Re: Find the number of integer solutions

    thank you for your help
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  5. #5
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    Re: Find the number of integer solutions

    If you require all x's to be 0 or greater, the equation is ((N-1)C(K-1)).
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