Binomial expansion of binomial terms

Given expression:

$\bigg(ab(c+d)+cd(a+b)\bigg)^{10}$

$=\bigg(abc+abd+cda+cdb\bigg)^{10}$

$=\bigg(abcd\bigg)^{10}\bigg(\frac1a+\frac1b+\frac1c+\frac1d\bigg)^{10}$

The co-efficient of $a^8b^4c^9d^9$ in the expansion of the expression above would same as the co-efficient of $\dfrac{1}{a^2}\dfrac{1}{b^6}\dfrac{1}{c}\dfrac{1}{d}$ in $\bigg(\frac1a+\frac1b+\frac1c+\frac1d\bigg)^{10}$ which is equal to $\dfrac{10!}{2!\cdot6!\cdot1!\cdot1!} = \boxed{2520}$ .