You haven't said what database access technology you're using so I'm just going to show you the raw SQL. If you are using something specific like ADO.net, LinqtoSQL, Entity Framework, NHibernate etc then you really should mention these things in your question as it often makes all the difference.
Add a bit\Boolean "locked" field to the Professor database and when you retrieve the professor
UPDATE Professor SET Locked = 1 WHERE ID = 123
SELECT * From Professor WHERE ID = 123
Then when the user chooses to not accept that professor to view
UPDATE Professor SET Locked = 0 WHERE ID = 123
You then update the sql that shows the list of available professors to exclude those that are locked
SELECT * From Professor WHERE Locked = 0