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Applying boundary conditions to counting combinatorial question [duplicate]
I was trying to count the number of natural number solutions to the equation: $x_1 + x_2 + ... + x_{11} = 20$, such that $0 \leq x_i \leq 9$, for all $i \in \{1, ..., 11\}$.
I know how to apply the ...
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How many distinct, non-negative integer solutions are there for $2x_0+\sum_{i=1}^{m}{x_i}=n$?
We are given constants $m$ and $n$. How many non-negative integer solutions are there for $2x_0+\sum_{i=1}^{m}{x_i}=n$ satisfying the condition that$x_i\neq x_j$ if $i\neq j$?
I thought a good first ...
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