Question 555629: I am trying to figure out what formula to use on this question and also how to proceed with the formula.
A password to a computer is to consist of 2 lower case letters followed by three digits. How many different passwords are possible if repetition of letters and numbers is not permitted?
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A password to a computer is to consist of 2 lower case letters followed by three digits. How many different passwords are possible if repetition of letters and numbers is not permitted?
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The 1st letter is 1 of 26, the 2nd is 1 of 25.
The 1st digit 1 or 10, then 9, then 8.
--> 26*25*10*9*8 = 468000
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Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! It's better if you reason it out and
don't think of it as a formula.
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Imagine you have 5 empty boxes that you can put
things in, but you are restricted as to what you can
put in them.
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There are 26 possible things ( letters ) you can put in the 1st box
You have used up a letter, so you only have 25 possible letters
you can put in the 2nd box.
In the 3rd box, you are allowed 0 - 9, so there are 10 possible things
In the 4th box, you have 10 - 1 = 9 possible things allowed
In the 5th box, you have 10 - 2 = 8 possible things allowed
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The numbers of things allowed in the 5 boxes is:
26, 25, 10, 9, and 8
Now the key to the problem is what to do with these numbers.
The general rule is, whenever you have
( x number possible ) AND ( y number possible ) AND ( z number possible ) etc. etc. etc.
The resulting possibilities are x times y times z etc.
So, the number of possible passwords is:
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