The coefficient of ${\mathrm{a}}^8{\mathrm{b}}^4{\mathrm{c}}^9{\mathrm{d}}^9$ in ${(\mathrm{abc}+\mathrm{abd}+\mathrm{acd}+\mathrm{bcd})}^{10}$

$$\begin{gathered} \left(\mathrm{abc}+\mathrm{abd}+\mathrm{acd}+\mathrm{bcd}\right) \\ {\left(\mathrm{abcd}\right)}^{10} {\left(\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}+\frac{1}{\mathrm{c}}+\frac{1}{\mathrm{d}}\right)}^{10} \\ {\mathrm{a}}^8{\mathrm{b}}^4{\mathrm{c}}^9{\mathrm{d}}^9={\left(\mathrm{abcd}\right)}^{10}{\left(\frac{1}{\mathrm{a}}\right)}^2{\left(\frac{1}{\mathrm{b}}\right)}^6{\left(\frac{1}{\mathrm{c}}\right)}^1\left(\frac{1}{\mathrm{d}}\right) \end{gathered}$$

cofficient will be

$$\begin{gathered} =\frac{10!}{2!6!1!!} \\ =2520 \end{gathered}$$