For a positive integer $n$ if the mean of the binomial coefficients in the expansion of $(a+b{)}^{2n-3}$is 16,  then $n$ is equal to :

Mean of binomial coefficients in the expansion of 

$(a+b{)}^{2n-3}$ is 

$\begin{array}{l}\frac{1}{2n-3+1}\left[{ }^{2n-3}{C}_0{+}^{2n-3}{C}_1+\dots {+}^{2n-3}{C}_{2n-3}\right]\\ =\frac{1}{2(n-1)}{2}^{2n-3}=\frac{2^{2(n-2)}}{n-1}=16=2^4\\ \Rightarrow n=5\end{array}$