Question

Coefficient of $x^{12}$ in ${\left(1+x^3\right)}^5{\left(1+x^4\right)}^8{\left(1+x^5\right)}^{11}$ is

Answer 1

Answer: 501

Possible powers of $x$
in ${\left(1+x^3\right)}^5=0,3,6,9,12,\dots {\left(1+x^4\right)}^8$
$=0,4,8,12,\dots$ and in ${\left(1+x^5\right)}^{11}=0,5,10,\dots$
Possibilities for $x^{12}$ is

$\Rightarrow 501$