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 :

Solution:

Mean of binomial coefficients in the expansion of

$(a + b)^{2 n - 3}$ is

$\begin{array}{l} \frac{1}{2 n - 3 + 1} [^{2 n - 3} C_{0} +^{2 n - 3} C_{1} + \dots +^{2 n - 3} C_{2 n - 3}] \\ = \frac{1}{2 (n - 1)} 2^{2 n - 3} = \frac{2^{2 (n - 2)}}{n - 1} = 16 = 2^{4} \\ \Rightarrow n = 5 \end{array}$

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

Solution:

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