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How many integer solutions are there to the equation $x + y + z = 8$ for which

$x\text{,}$ $y\text{,}$ and $z$ are all positive?

$x\text{,}$ $y\text{,}$ and $z$ are all non-negative?

$x\text{,}$ $y\text{,}$ and $z$ are all greater than or equal to $-3\text{.}$

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