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Find the number of 5-lists of the form (x1, x2, x3, x4, x5), where each xi...

Find the number of 5-lists of the form (x1, x2, x3, x4, x5), where each xi is a nonnegative integer and x1 + x2 + x3 + x4 + 3x5 = 12.

Does this have to be answered by cases or is there a systematic way to determine all of the possibilities?

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