# The coefficient of $x^{32}$ in the expansion of $(x^4-\large\frac{1}{x^3})^{15}$ is

$\begin{array}{1 1}(A)\;-15C_3\\(B)\;15C_4\\(C)\;-15C_5\\(D)\;15C_2\end{array}$

Toolbox:
• $T_{r+1}=nC_r a^{n-r} b^r$
$T_{r+1}=15C_r (x^4)^{15-r}(-x^{\Large\frac{1}{3}})^r$
$\Rightarrow 15C_r x^{60-4r-3r}(-1^r)$
$\Rightarrow 15C_r (-1)^r x^{60-7r}$
$\Rightarrow 60-7r=32$
$\Rightarrow r=4$
$\therefore T_{r+1}=T_{4+1}=15C_4 (-1)^4x^{32}$
$\therefore$ Required coefficient =$15C_4$
Hence (B) is the correct answer.