Until 2005, the UPC bar code had 14 digits (0–9). The first four digits represent the manufacturer, the next nine represent the product, and the last is a check digit. (a) How many different manufacturers could be encoded? Number of manufacturers __________ (b) Per manufacturer, how many different products can be encoded? Number of products ___________ (c) In 2005, the EAN bar code replaced the UPC bar code, adding a 15th digit. If this new digit is used for product identification, how many different products per manufacturer can be encoded? Number of products __________
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Until 2005, the UPC bar code had 14 digits (0–9). The first four digits represent the manufacturer, the next nine represent the product, and the last is a check digit.
(a) How many different manufacturers could be encoded?
Number of manufacturers __________
(b) Per manufacturer, how many different products can be encoded?
Number of products ___________
(c) In 2005, the EAN bar code replaced the UPC bar code, adding a 15th digit. If this new digit is used for product identification, how many different products per manufacturer can be encoded?
Number of products __________
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