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Math Help - NUmber of solutions

  1. #1
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    NUmber of solutions

    How many solutions does this equation x1+x2+x3 = 11, given x1,x2,x3 >0 have?

    This is solved using combination.

    How can this be solved.
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  2. #2
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    See Theorem one in this Wikipedia article.
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  3. #3
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    Thanks.


    But it is not matching with the answer given.

    By using that theorem, it would taken two from 10 available gaps, 10C2.

    But i have the answer as 13c11.

    I think they are considering it as X1,X2,X3 >=0. So we can have 13 gaps and 13C2 which is equal to 13C11.

    I dont know whether my understanding is wrong , please correct.
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  4. #4
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    You may be right. However, if in fact there no mistake in the problem statement, could you post an update here when you find out what's going on?
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  5. #5
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    Thanks a lot. And sure i'll update if find anything wrong about the question.
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  6. #6
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    Hello, kumaran5555!

    How many solutions does this equation have: . x_1+x_2+x_3\:=\:11
    . . given x_1,x_2,x_3 \,>\,0

    Consider an eleven-inch board marked in one-inch intervals.

    . . . . \square\!\square\!\square\!\square\!\square\!\squa  re\!\square\!\square\!\square\!\square\!\square

    It can be divided into three nonzero pieces
    . . by choosing any two of the ten inch-marks
    . . and cutting the board there.

    Therefore, there are: . \displaystyle _{10}C_2 \:=\:{10\choose2} \:=\:\frac{10!}{2!\,8!} \:=\:45\text{ solutions.}

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