A function $f:\left\{0, 1\right\}^{n}\rightarrow \left\{0, 1\right\}$ is called symmetric if for every $x_{1}, x_{2},....,x_{n} \in \left\{0, 1\right\}$ and every permutation $\sigma$ of $\left\{1, 2,...,n\right\}$, we have
$f\left(x_{1}, x_{2},...,x_{n}\right) = f \left(x_{\sigma(1)}, x_{\sigma(2)},....x_{\sigma(n)}\right)$.
The number of such symmetric function is:
- $2^{n+1}$
- $2^{n}$
- $2^{2n}/n!$
- $2^{2n}$
- $n!$