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Omni-MATH / Let π be a randomly chosen permutation of the numbers from 1 through 2012. Find the probability that π(π(2012))=2012.

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problem

Let π\pi be a randomly chosen permutation of the numbers from 1 through 2012. Find the probability that π(π(2012))=2012\pi(\pi(2012))=2012.
Plain-text mathematical notation (without MathML)
Let π be a randomly chosen permutation of the numbers from 1 through 2012. Find the probability that π(π(2012))=2012.
Original LaTeX notation
Let $\pi$ be a randomly chosen permutation of the numbers from 1 through 2012. Find the probability that $\pi(\pi(2012))=2012$.

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