computing probability of pairing Alice has $n$ pairs of socks with $n$ colors ranging in shades of grey enumerated from $1$ to $n$. She takes the socks out of the drier and pairs them randomly. We will assume in each pair,the right and the left socks are identical.
Assume that Alice finds the pairing acceptable if all the socks are paired correctly.
Show that the probability of this event is:
$$ \frac{2^nn!}{(2n)!}$$
I have this question in one of my classes but I think what we are asked to prove is wrong. I think the probability that the pairing is acceptable is $\frac{1}{n!}$. Maybe I am missing something and making a fool of myself. Need some help!

The question assumes you can't tell the difference between right and left socks.
So there are $2n-1$ possible socks to match with the first sock, not $n$.
