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Inclusion-exclusion principle: Number of integer solutions to equations

This is a problem that I have had much trouble with. If you attempt in helping me with this, please explain step by step and present your formulas. It will be greatly appreciated.

Find the number of integer solutions to: $$x_1+x_2+x_3+x_4=25$$ satisfying: $$\begin{array}{rcccl} 0&\leq &x_1 &\leq& 7\\ 3 &\leq & x_2 & \leq &5\\ 4 &\leq & x_3 & \leq & 8\\ -2 & \leq& x_4 & \leq & 2. \end{array}$$

Please emphasize on how to use the inclusion exclusion principle. Thanks.

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    This looks very similar to http://math.stackexchange.com/questions/34871/inclusion-exclusion-principle-number-of-integer-solutions-to-equations/34873#34873 Did you respond to the earlier answer there?2011-04-25
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    I've added a bit to that earlier answer. Really, posting this new question is not in the spirit of this site. Keep it all in one place.2011-04-25
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    There is no answer to this question... The total sum of the largest values of those variables is 22.2013-09-23

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