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I am having problems analyzing the number of solutions to the equation of the form

$$x_1 + x_2 +x_3 +x_4 + x_5 +x_6 < 10$$

also if you can generalize the result and post some relevant links from where I can study i will be grateful. Thanks in advance.

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    Do you intend for the $x_i$ to be non-negative integers? If so, you should take a look at [Partition Numbers](http://en.wikipedia.org/wiki/Partition_(number_theory)).2011-11-29
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    yes xi >= 0 in every case well can't this problem be solved using combinatorics2011-11-29
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    See http://math.stackexchange.com/questions/9386/number-of-possible-solutions-for-an-equation and http://math.stackexchange.com/questions/40640/how-many-solutions-possible-for-the-equation-x-1x-2x-3x-4x-5-55-if2011-11-29

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