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I am not that great at math, but am still interested in how one would go about calculating the following question:

Employees can type in their access code. There are two sets: A,B,C,D,E and 1,2,3,4,5. An access code looks like this: E314. So always one letter at the beginning, then 3 numbers. There are 350 employees. Are there enough unique access codes for every person?

Now, I tried looking this up, but I couldn't find how this should be calculated when there are fixed positions, i.e. the letter at the start of any access code.

Thanks in advance!

stijuh
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  • As to the usefulness of these access codes, it seems like a rather poor system unless it had multifactor authentication of some sort since someone could just come up and press random buttons and have a very high chance of having correctly guess a code that is in use – JMoravitz Aug 29 '22 at 18:24

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This follows directly from the rule of product which loosely paraphrased says that if every outcome can be described uniquely by a sequence of steps where the number of options per step does not change based on previously made choices, then the total number of outcomes is the product of the number of options for each step. Here, there are $5$ options for the starting letter, $5$ options for the first number, $5$ options for the second number, and $5$ options again for the third number for $5^4$ total outcomes.

JMoravitz
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