The expansion of \((ax-2)^4\left(1+\frac{b}{x}\right)^3\) is written in descending powers of \(x\).

The first 3 terms of this expansion are \(81x^4+999x^3+cx^2\).

It is given that \(a\), \(b\) and \(c\) are positive integers.

Find the values of \(a\), \(b\) and \(c\).