Question

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

• A. 440
• B. 770
• C. 990
• D. 1001

Answer 1

The Correct Option is C

We have coefficient of $x^4$ in $(1 + x + x^2 + x^3)^{11}$
= coefficient of $x^4$ in $(1 + x^2)^{11} (1 + x)^{11}$
= coefficient of $x^4$ in $(1 + x)^{11}$ + coefficient of $x^2$ in
$ 11. (1 + x)^{11}$ + constant term is $^{11}C_2. (1 + x)^{11}$
$ = {^{11}C_4} + 11 . {^{11}C_2} + {^{11}C_2} = 990 $