The coefficient of x 18 in the expansion of x 4 - 1 x 3 15 is _ _ _ _ _ _ _ _ _ _ _ _

Given,

Binomial expression ${\left(x^4-\frac{1}{x^3}\right)}^{15}$

Now general term is given by,

$T_{r+1}={}^{15}C_r{\left(x^4\right)}^{15-r}{\left(-\frac{1}{x^3}\right)}^r$

$\Rightarrow T_{r+1}={}^{15}C_r{x}^{60-7r}(-1{)}^r$

For coefficient of $x^{18},$ equate $60-7r=18$

$\Rightarrow r=6$

Coefficient of $x^{18}={\left(-1\right)}^6·{}^{15}C_6=5005$