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Combinatoricshard
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Find the number of non-negative integer solutions to x1+x2+x3+x4+x5=12x_1 + x_2 + x_3 + x_4 + x_5 = 12x1​+x2​+x3​+x4​+x5​=12 such that each xi≥1x_i \geq 1xi​≥1.