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What is the generating function for the number of non-negative integer solutions to x1 + x2...

What is the generating function for the number of non-negative integer solutions to
x1 + x2 + x3 + x4 + x5 = 50
if:

1.) There are no restrictions
2.) xi >= 2 for all i

3.) x1 <= 10

4.) xi <= 12 for all i

5.) if x1 is even

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