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ISI 2019 | PCB CS | Question: 13

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An $n$-variable Boolean function $f:\{0,1\}^{n} \rightarrow\{0,1\}$ is called symmetric if its value depends only on the number of $1 \text{'s}$ in the input. Let $\sigma_{n}$ denote the number of such functions.

  1. Calculate the value of $\sigma_{4}$.
  2. Derive an expression for $\sigma_{n}$ in terms of $n$.
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