Question 330386: A password consists of three digits, 0-9, followed by 3 letters from an alphabet having 26 letters. If repetition of digits is allowed, but repitition of letters is not allowed, determine the number of different passwords that can be made.
Answer by neatmath(302)   (Show Source):
You can put this solution on YOUR website!
This problem involves some statistical reasoning and knowledge, but there is a very simple solution to it.
We know that there are 10 digits, and 26 letters available. We can repeat digits, but not letters, thus our password should look something like this, where N is a number, and L is a letter:
NNNLLL
Then we will fill in the number of choices available for each character in the password:
10*10*10*26*25*24
When we multiply these numbers out, we will have the total number of possible passwords:
15,600,000
There are 15,600,000 possible passwords based on the given criteria.
As a bonus, if we were not allowed to repeat digits, then we would have:
10*9*8*26*25*24 or 11,232,000 possible passwords.
There is a whole lot more to this subject, but I hope this helps you get started! :)
|
|
|
