Does \(n\) matter?

Algebra Level 4

Find the value of :

\({ \{ { (C }_{ 0 }+{ C }_{ 3 }+...)-\frac { 1 }{ 2 } ({ C }_{ 1 }+{ C }_{ 2 }+{ C }_{ 4 }+{ C }_{ 5 }+....)\} }^{ 2 }+\\ \frac { 3 }{ 4 } { \{ { C }_{ 1 }-{ C }_{ 2 }+{ C }_{ 4 }-{ C }_{ 5 }.....\} }^{ 2 }\)

\({ C }_{ r }\quad represents\quad \frac { n! }{ r!(n-r)! } \)

And if you feel that the answer must depend on \(n\), give \(1729\) as your answer!

\(This\quad problem\quad is\quad not\quad original\)

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