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The password must be $7$ characters long and it can include the combination: $10$ digits $(0-9)$ and uppercase letters $(26)$.

My Solution:

Thus in total there are $7$ slots, each slot could be either $0-9$ or $26$ letters $= 36$ possibilities for each slot, therefore, $36^7$ would be the number of password combinations?

Am I correct?

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    $\begingroup$ Yes. ${}{}{}{}$ $\endgroup$ – copper.hat Feb 16 '16 at 6:16
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Your solution is correct. You can also look at this as a function from a set with $7$ elements to a set with $36$ elements.

How many functions are there from a $7$ element set to a $36$ element set?

For each element in the domain, how many elements in the codomain can it possibly get mapped to? $36$

Since there are $7$ elements in the domain, there are a total of $$36 \cdot 36 \cdot 36 \cdot 36 \cdot 36 \cdot 36 \cdot 36=36^7$$ possible functions.

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You are correct. $36^7$ is the right answer.

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    $\begingroup$ You may as well write that as a comment. $\endgroup$ – barak manos Feb 16 '16 at 6:47
  • $\begingroup$ Oh.. I am sorry.. I am new here $\endgroup$ – user313384 Feb 16 '16 at 6:54

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