How many solutions are there to the inequality x1+x2+x3+x4≤15, where x1,x2,x3, and x4 are nonnegative integers? Hint: Introduce an extra variable x5 and consider x1+x2+x3+x4+x5 = 15.

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$N=C^{15}_{5+15-1}=C^{15}_{19}=\frac{19!}{15!4!}=3876$

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