The arithmetic mean of nC0,nC1,…,nCn, is

The arithmetic mean of $^{n} C_{0},^{n} C_{1}, \dots,^{n} C_{n},$ is

A
$\frac{1}{n}$
B
$\frac{2^{n}}{n}$
C
$\frac{2^{n - 1}}{n}$
D
$\frac{2^{n + 1}}{n}$

Solution:

Clearly, Required mean $= \frac{^{n} C_{0} +^{n} C_{1} + \dots +^{n} C_{n}}{n} = \frac{2^{n}}{n}$

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