Question

Coefficient of x18 in (x4 - $\frac{1}{x^{3}}$)15

Answer 1

The answer is $6$
$T_{r+1}=^{15}C_{r}(x^{4})^{15-r}(-\frac{1}{x^{3}})^{r}$
$T_{r+1}=^{15}C_{r}(-1)^{r}x^{60-7r}$
$60-7r=18\Rightarrow r=6$
$T_{7}=^{15}C_{6}(-1)^{6}x^{18}$
$T_{7}=^{15}C_{6}x^{18}$
So, the Coefficient of x18 is 15C6