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This question is related to Error solving “stars and bars” type problem
I have what I thought is a fairly simple problem: Count non-negative integer solutions to the equation
$$x_1 + x_2 + x_3 + x_4 + x_5 = 23$$
such that $0 \leq x_1 \leq 9$.
The difference here is on the constraint. It bounds all the $x_i$ under 10 : $\forall i\le5$ , $0 \leq x_i \leq 9$.
$8+8+0+0+7=23$ is accepted but not $18+3+0+0+2=23$ or $11+0+0+0+12=23$ . In other words all the $x_i$ must be usual digits.
Note that bad solutions may include one or two bad $x_i$. It is the main difficulty.
What is the count of combinations ?
Edit : this question includes a double bounds and a supplemental difficulty to find the right solution.