Computer Password (number of combinations)

J

jonboy

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Jun 8, 2006
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A computer password consists of 4 characters. The characters can be one of the 26 letters of the alphabet. Each character may be used more than once. How many different passwords are possible?
The answer is 456,976 but I have no clue how to get it.

I know I would use:

. .n!
------
(n-r)!

I thought I would fill in the following because we have 26 letters and the list is 4 characters.

. .26!
---------
(26-4)!

What did I do wrong? My answer it totatlly not the same..
 
Your way does not allow the same letter to appear more than once, jonboy;
does not include combos like aabc and aaab and aaaa: capish ?
 
So whenever I have x amount of objects and the the list is a long and they can be repeated, then the formula is always x^a??
 
YES.

Take 2 letters out of a,b,c; 3^2 = 9; the combos are:
ab,ba,ac,ca,bc,cb,aa,bb,cc

OK :?: :idea:
 
jonboy said:
So whenever I have x amount of objects and the the list is a long and they can be repeated, then the formula is always x^a??
Click to expand...
That is called the multiplication rule: it should be in your text material.
If I have a string of thing to do, the number of ways to do it is found by multiplying the number of ways to do each step in the string.
In this case, you are to pick a letter four times.
Each time you have 26 choices.
 
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