Until 2005, the UPC bar code had 12 digits (09). The first six digits represent the manufacturer,

Question:

Until 2005, the UPC bar code had 12 digits (09). The first six digits represent the manufacturer, the next five represent the product, and the last is a check digit.
(a) How many different manufacturers could be encoded?
(b) How many different products could be encoded?
(c) In 2005, the EAN bar code replaced the UPC bar code, adding a 13th digit. If this new digit is used for product identification, how many different products could now be encoded?