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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.