The coefficient of ${\mathrm{a}}^{10}{\mathrm{b}}^7{\mathrm{c}}^3$ in the expansion of $(\mathrm{bc}+\mathrm{ca}+\mathrm{ab}{)}^{10}$ is

$(\mathrm{bc}+\mathrm{ca}+\mathrm{ab}{)}^{10}$

General term $=\frac{10!}{\mathrm{p}!\mathrm{q}!\mathrm{r}!}\left(\mathrm{bc}{)}^{\mathrm{p}}\right(\mathrm{ca}{)}^{\mathrm{q}}(\mathrm{ab}{)}^{\mathrm{r}}=\frac{10!}{\mathrm{p}!\mathrm{q}!\mathrm{r}!}{\mathrm{a}}^{\mathrm{q}+\mathrm{r}}\cdot {\mathrm{b}}^{\mathrm{r}+\mathrm{p}}.{\mathrm{c}}^{\mathrm{p}+\mathrm{q}}$

Let $\mathrm{q}+\mathrm{r}=10,\mathrm{r}+\mathrm{p}=7,\mathrm{p}+\mathrm{q}=3\therefore \mathrm{p}=0,\mathrm{q}=3,\mathrm{r}=7$

$\therefore$ coefficient of ${\mathrm{a}}^{10}{\mathrm{b}}^7{\mathrm{c}}^3\text{ is }\frac{10!}{0!3!7!}=\frac{0.9.8.7!}{1.1\cdot 2\cdot 3\cdot 7!}=120$