All you need is actually just 3 tables:
1) table with the customer information (customerID, name, age, etc)
2)Lookup table for the proffessions (professionId, professionName, etc)
3) table for CustomerProffessions (custommerProffessionId, etc)
Make sure that the CustomerProffessions table has 2 foreign keys: customerID and professionId. That solves your problem nicely, dont you think?