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 ${ }^{18} C_{8}$