The coefficient of $x^{8} y^{10}$ in the expansion of $(x + y)^{18}$ is:
The coefficient of $x^{8} y^{10}$ in the expansion of $(x + y)^{18}$ is:
None of these.
\({^\text{18}}\text{C}_{\text{8}}\)
\(2^{18}\)
\({^\text{18}}\text{p}_{\text{10}}\)
Solution
Solution:Suppose (r + 1)th term in the given expansion is independent of x.Then, we have\(\text{T}_{\text{r}+1}={^\text{18}}\text{C}_{\text{r}}(\text{x})^{18-\text{r}}\ \text{y}^{\text{r}}\)For this term to be independent of x, we must have\(\text{r}=10\)Hence, the required coefficient is \({^\text{18}}\text{C}_{\text{10}}\)or\({^\text{18}}\text{C}_{\text{8}}\)