The coefficient of $x^4$ in expansion of $(1 + x + x^2 + x^3)^{11}$ is …
🎥 Video solution / Text Solution of this question is given below:
We can write generating function $f(x) = (1 + x + x^2 + x^3)^{11}$.
Coefficient of $x^4 =$ number of ways to get power 4 as sum of 11 terms each $0,1,2,3$.
By multinomial expansion, coefficient of $x^4 = {}^{11}C_4 + 10{}^{11}C_3 + 6{}^{11}C_2 + {}^{11}C_1 = 990$.