Argh... Not this again!

Algebra Level 3

What is the co-efficient of \({ x }^{ 53 }\) in the expansion \(\displaystyle \sum _{ m=0 }^{ 100 }{ \begin{pmatrix} 100 \\ m \end{pmatrix} } { (x-3) }^{ 100-m }{ .2 }^{ m }\)?

Here \(\begin{pmatrix} a \\ b \end{pmatrix}\) means the number of ways of choosing \(b\) objects from \(a\).

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