A company has a specific way of bar coding products purchased from suppliers. It

Question

A company has a specific way of bar coding products purchased from suppliers. It involves an 8 digit number (digits from 0 – 9). The first 3 digits represent the supplier, and the next 4 digits represent the product. The last digit represents a “check number” (a value to help identify if a typo has occurred).

a) How many different suppliers are able to be encoded?

b) How many different products can be encoded?

If you cannot repeat any of the digits in the supplier code, how many suppliers are able to be encoded now?

Explanation / Answer

(a) Suppliers:

3 digits:

1st digit is chosen in 10 ways: 0 to 9.

2nd digit also in 10 ways: 0 to 9, since repetition is allowed.

3rd digit also in 10 ways.

So, total number of sppliers = 10 x 10 X 10 = 1000

(b) Products:

4 digits.

Arguing as above,

number of different products = 10 X 10 X 10 X10 = 10000

(c) If you cannot repeat any of the digits in the suppier code:

supplier = 3 digita.
st digit in 10 ways

2nd digit in 9 ways

3rd digits in 8 ways.

So, total number of suppliers = 10 X 9 X 8 = 720

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