Sum of powers

Algebra Level 3

\[ \begin{cases} a+b+c=1\\ { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=21\\ { a }^{ 3 }+{ b }^{ 3 }+{ c }^{ 3 }=55 \end{cases} \]

Given that \(a,b\) and \(c\) satisfy the system of equations above, find \((a-1)(b-1)(c-1) \).

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