If 19 get their hat, won't the 20th also? There won't be another hat to get mixed up with... So... 1/(20!) ? It's been awhile since I've mathed. Could be way of

If 19 get their hat, won't the 20th also? There won't be another hat to get mixed up with... So... 1/(20!) ? It's been awhile since I've mathed. Could be way off. Is this your homework?