Online IDs As the customer base at OHaganBooks.com grows, IT manager Ruth Nabarro is thinking of introducing identity codes for all the customers, using capital letters and/or numbers. Help her answer the questions in Exercises 37–40.
O’Hagan sends Nabarro the following memo:
To: Ruth Nabarro, Software Manager
From: John O’Hagan, CEO
Subject: Customer identity Codes
I have read your proposal for the customer ID codes. However, due to our ambitious expansion plans, I would like our system software to allow for at least 500,000 customers. Please adjust your proposal accordingly.
Nabarro is determined to have a sequence of letters followed by some digits, and, for reasons too complicated to explain, there cannot be more than two letters, the letters must be different, the digits must all be different, and the first digit cannot be a zero. What is the form of the shortest code she can use to satisfy the CEO, and how many different customers can be identified?
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