Let Y admissions know in writing. Then have the correct one faxed over, if possible, and be on the phone with the person receiving the fax, in real time. Ask them to file the correct letter and destroy the wrong one while you are on the phone. Short of this, if they won't receive the fax rec and insist on snail mail/sealed envelope, call once you know the correct letter must have been received. Ask them to replace and destroy as above.
Or if you're really bold you could ask them to forward the P letter over to P, but that's a bit of a risk
They want to read your correct file, mahedonist, not look for a reason to boot you.
The person filing these things won't be evaluating your application. They may laugh at you, but it won't impact your chances!