Let $X$ be a set containing $n$ elements. If two subsets $A$ and $B$ of $X$ are picked at random, the probability that $A$ and $B$ have the same number of elements, is

  • A

    $\frac{{^{2n}{C_n}}}{{{2^{2n}}}}$

  • B

    $\frac{1}{{^{2n}{C_n}}}$

  • C

    $\frac{{1\,.\,3\,.\,5......(2n - 1)}}{{{2^n}}}$

  • D

    $\frac{{{3^n}}}{{{4^n}}}$

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