How to take the limit $N \rightarrow \infty$ and $q \rightarrow \infty$ of the expression $\binom{N}{q}$ such that $\frac{q^{2}}{N}= \lambda$. Can I substitute $N = \frac{q^2}{\lambda}$ and then take $q \rightarrow \infty$ in the resulting equation? Is this a valid step to do?
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