Limited X

Algebra Level 3

If $$0\le { x }_{ 1 }<6 , { x }_{ 2 }\ge 0$$ , and $${ x }_{ 3 }>5$$. Then, how many solutions so that $${ x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 }=17$$?

$${ x }_{ 1}, { x }_{ 2 }, { x }_{ 3}$$ are integers

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