$\text{ The sum of the coefficients of }(x+y{)}^n\text{ is }32,\text{ then greatest coefficient is }$

$\text{ The sum of the coefficients of }(x+y{)}^n\text{ is }32$

$\Rightarrow 2^n=32=2^5$

$\Rightarrow n = 5$

$\therefore \text{ Greatest coefficient is }{}^{n}C_{\frac{\left(n-1\right)}{2}}={}^{5}C_{\frac{5-1}{2}}={}^{5}C_2=10$