# 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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