The coefficient of  $x^4$ in the expansion of ${(1+x+x^2+x^3)}^{11}$ is

Given that, ${(1+x+x^2+x^3)}^{11}$

$\begin{array}{l}={[1+x+x^2(1+x)]}^{11}={\left[(1+x)(1+x^2)\right]}^{11}\\ ={(1+x)}^{11}{(1+x^2)}^{11}c\\ =(1+{}^{11}{C}_{1}x+{}^{11}{C}_2{x}^2+{}^{11}{C}_3{x}^3+{}^{11}{C}_4{x}^4+\cdots )(1+{}^{11}{C}_1{x}^2+{}^{11}{C}_2{x}^4+\cdots )\end{array}$

Coefficient of $x^4$  is $=1{}^{11}{C}_2+{}^{11}{C}_4+{}^{11}{C}_2\cdot {}^{11}{C}_1$

$=55+336+605=990$