SOLUTION: in how many distinct ways can a 5-digit password be made using two letters and three numbers if no repeats are allowed?

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Question 1140203: in how many distinct ways can a 5-digit password be made using two letters and three numbers if no repeats are allowed?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

Read attentively on how I re-formulated your original post to make sense. 

    in how many distinct ways can a highlight%28cross%285-digit%29%29 5-symbol  password be made using 
    two letters and three highlight%28cross%28numbers%29%29 digits if no repeats are allowed?


Solution 

You have 5 symbols : 5 = 2 letters + 3 digits,


so 5! = 120 permutations are possible.    ANSWER


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Two different readings and interpretations of your condition are possible.

1.   Two  fixed  letters and  3  fixed  digits are allowed / (are used). 
    
    It is exactly that reading and interpretation that I used in my solution.

and

2.   Any two letters of the English alphabet and any  3  digits of ten digits are allowed.

Then the solution should be different.

But just the fact that two different interpretations are possible makes this formulation  DEFECTIVE.