The coefficient of x
Question:

The coefficient of x8 y10 in the expansion of (x + y)18 is

(a) 18C8

(b) 18p10

(c) 218

(d) none of these

Solution:

(a) ${ }^{18} C_{8}$

Suppose the $(r+1)$ th term in the given expansion contains $x^{8} y^{10}$.

Then, we have

$T_{r+1}={ }^{18} C_{r} x^{18-r} y^{r}$

For the coefficient of $x^{8} y^{10}$ We have

$r=10$

Hence, the required coefficient is ${ }^{18} C_{10}$ or ${ }^{18} C_{8}$