25,43,56
37,53,64
45,70,98
44,54,65

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The probability of drawing exactly $n$ marbles can be calculated as the product of drawing $n-1$ white marbles followed by a red marble:

$P(n) = \frac{1}{2}\times\frac{2}{3}\times\dots\times\frac{n-1}{n}\times\frac{1}{n+1} = \frac{1}{n(n+1)}$

Solving $P(n) < \frac{1}{2010}$ gives us

$n(n+1) > 2010 \Rightarrow \boxed{n\geq45}$