The coefficient of ${\mathrm{x}}^4$ in the expansion of ${\left(1+\mathrm{x}+{\mathrm{x}}^2\right)}^{10}$ is ………

${\left(1+\mathrm{x}+{\mathrm{x}}^2\right)}^{10}{=}^{10}{\mathrm{C}}_0{+}^{10}{\mathrm{C}}_1\left(\mathrm{x}+{\mathrm{x}}^2\right){+}^{10}{\mathrm{C}}_2{\left(\mathrm{x}+{\mathrm{x}}^2\right)}^2{+}^{10}{\mathrm{C}}_3{\left(\mathrm{x}+{\mathrm{x}}^2\right)}^3\dots {+}^{10}{\mathrm{C}}_{10}{\left(\mathrm{x}+{\mathrm{x}}^2\right)}^{10}$

coefficient of ${\mathrm{x}}^4$ is ${ }^{10}{\mathrm{C}}_2\left(1\right){+}^{10}{\mathrm{C}}_3\left(3\right){+}^{10}{\mathrm{C}}_4\left(1\right)=45+360+210=615$