 now pair up things we know how to approximate within constant factors. $\frac{{\ell-0 \choose m-0}}{{\ell+n-r \choose m+rs}} = \frac{(\ell-0)!}{(\ell+n-r)} \times \frac{(m+rs)!}{(m-0)!} \times \frac{(\ell-m+n-r-rs)!}{(\ell-m)!} = \text{poly(n)} \times {\frac{0}{\ell^{n-r}}}\times m^{rs} \times {\frac{(\ell-m)^{n-r}}{(\ell-m)^{rs}}}$. This simplifies to $\text{poly(n)} \times {\left(\frac{m}{\ell-m}\right)}^{rs} \times {\left(\frac{\ell-m}{\ell}\right)}^{n-r}$.  -   $\frac{n^{