Browse Questions

# Find the coefficient of $x^5$ in $(x+3)^8$

$\begin{array}{1 1}(A)\;1521\\(B)\;1512\\(C)\;1571\\(D)\;1581\end{array}$

General term in $(x+3)^8=8C_rx^{8-r}3^r$
We have to find the coefficient of $x^5$
$8-r=5$
$-r=5-8$
$-r=-3$
$r=3$
$\therefore$ Coefficient of $x^5$ (putting r=3)
$\Rightarrow 8C_3.3^3$
$\Rightarrow \large\frac{8!}{3!5!}$$\times 3^3 \Rightarrow \large\frac{8\times 7\times 6\times 5!}{3\times 2\times 5!}$$\times 3\times 3\times 3$
$\Rightarrow 56\times27$
$\Rightarrow 1512$
Hence (B) is the correct answer.