$\text{ The coefficient of }{a}^5{b}^6{c}^7\text{ in the expansion of }(bc+ca+ab{)}^9\text{ is }$

$\begin{array}{l}(bc+ca+ab{)}^9\\ =\sum _{0\le r,s\le 9}\frac{9!}{r! s! (9-r-s)!}\left(bc{)}^r\right(ca{)}^s(ab{)}^{9-r-s}\\ =\sum _{\begin{array}{c}0\le r,s\le 9\\ \end{array}}\frac{9! a^{9-r}{b}^{9-s}{c}^{r+s}}{r! s! (9-r-s)!}\end{array}$

$\begin{array}{l}\text{ For coefficient of }{a}^5{b}^6{c}^7\text{ , we set }\\ 9-r=5,9-s=6,r+s=7\end{array}$

$\begin{array}{l}\Rightarrow r=4,s=3\\ \text{∴ required coefficient is }\\ \frac{9!}{4!3!2!}=\frac{9\times 8\times 7\times 6\times 5}{6\times 2}=1260\end{array}$