How do I find the number of nonnegative integer solutions to $x+y+z=11$ provided that $x\leq 3, y\leq 4, z\leq 6$ using the sum rule (counting)?
I know the answer is 6, but I'm having difficulty understanding why.
2026-04-02 01:05:50.1775091950
Find the number of non-negative integer solutions to $x+y+z=11$
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One way is to expand $$(1+x+x^2+x^3)(1+x+x^2+x^3+x^4)(1+x+x^2+x^3+x^4+x^5+x^6)$$ and get the coefficient of $x^{11}.$