Activity 2: Is the UPC-A Scheme Sufficient?
(Student Copy)

Part A

1. With your group, use counting to solve this problem:  If John has 3 pairs of pants and 4 shirts, how many different outfits can he wear?

2. If an interior decorator is designing the interior of an apartment building and has 3 colors to use as the primary wall color, 2 different tints to use for trim, and 4 different colors to use for accent purposes, how many different color schemes can be created?

3. Given that the manufacturer's part of a 12-digit bar code consists of 5 digits, any one of which may be 0 through 9 (repeated digits like 00220 are allowed), how many different companies can be coded into this UPC-A system?  Do you believe that this number is sufficient for the number of companies applying for a UPC-A number?

4. Find the number of car (not truck) license plates that can be made for any one particular county in Indiana.  The Indiana scheme is to put the number of the county (based on alphabetical order) first, a letter of the alphabet second, and a four digit number third (examples 26B2519 & 53F4471).

Part B

1. As of July 1, 1992, the number of digits designated for the manufacturer was increased to 7.  How many companies can now be coded? 

2. Let us assume for a minute that the calculation for the number of companies that can be coded is not sufficient.  Come up with your own bar code system to increase the number of companies that can be included.  Describe it below.  How many companies can be coded with your system?

3. Find 3 companies from the stock exchange section of the newspaper and assign them 5-digit numbers (or the appropriate number based on your system) numbers.