SOLUTION: A system designer is asked to design an inventory system for a hardware manufacturer. The manufacturer produces 57,826 different kinds of hardware. The system designer must decide

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Question 945755: A system designer is asked to design an inventory system for a hardware manufacturer. The manufacturer produces 57,826 different kinds of hardware. The system designer must decide on a way to identify the different kinds of hardware. Each id# is to begin with two letters of the alphabet. Any letter can be used except I,O,Z. The rest of the id# is to consist of digits. How many digits must the designer include in the id# format to ensure that each kind of hardware has a unique id#s?
Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website!

Let the answer be n We choose the first letter 23 ways. We choose the second letter also 23 ways. We choose the 1st digit any of 10 ways. We choose the 2nd digit any of 10 ways. We choose the 3rd digit any of 10 ways. ... ... We choose the nth digit any of 10 ways. That's to n factors of 10. Divide both sides by 529 The smallest number of digits the designer can use is 5. Edwin