My shoe is missing!

A group of \(N\) people with distinct pairs of shoes attended a party. But when they left, they randomly took a pair of one left shoe and one right shoe. Let the probability of none of them getting both shoes of the same pair be \(P\).

Let \(\displaystyle \lim_{N\rightarrow \infty} P = X \).

Find the value of \(\ln(X)\).

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