Question 746487: "Determine how many different computer passwords are possible if the given number of digits (0-9) and the letters (A-Z) can be repeated and cannot be repeated."
5 digits followed by 2 letters
Repeated:
Not repeated:
I tried an example for repeated - 2-2-2-2-2-B-B but am not sure if that is correct or how to finish the problem.
Thank You.
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Case 1: Repetition allowed
There are ten possible digits, 0 through 9, so there are ten ways to choose the first digit. Then for each of those ways, since repetition is allowed, there are 10 ways to choose the second digit. Hence there are 10 times 10 or 100 ways to choose the first two digits. For each of those 100 ways there are 10 ways to choose the 3rd digit...and so on, so there are  ways to choose the 5 digits. Then, for each of those ways there are 26 ways to choose the first letter...and so on. Altogether:  different combinations. You can do your own arithmetic.
Case 2: Repetition prohibited
There are ten possible digits, 0 through 9, so there are ten ways to choose the first digit. Then for each of those ways, since repetition is not allowed, there are only 9 ways to choose the second digit since one of the 10 has already been used picking the first digit. Then there are 8 ways to pick the third digit...and so on. So there are  ways to pick the five digits, then similarly there are  ways to pick the two letters, so altogether:  different combinations. Again, you can do the arithmetic yourself.
Super Double Plus Extra Credit -- Case 3: Repetition demanded
How many combinations are possible if at least one repetition must occur somewhere in the combination?
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! "Determine how many different computer passwords are possible if the given number of digits (0-9) and the letters (A-Z) can be repeated and cannot be repeated."
If it's not "case sensitive," ie, if A = a, then there are 26 letters.
5 digits followed by 2 letters
Repeated: = 10*10*10*10*10*26*26
= 67600000
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Not repeated: = 10*9*8*7*6*26*25
You can multiply that.
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