Question 742385: Hi tutors, I've tried a couple of ways with this question and get 2 different answers, can you show me the right way, please?
Q: How many different 6 character computer passwords can be formed using upper & lower case letters and 0-9 numbers.
I know I've got 62 symbols and have used P(62,6) =62!/(62-6)! = ??
My answers are 5.6800325590x10^10 and 4.426165368x10^10.
Thanks always.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! PREACHY RANT (optional reading):
 is a formula you may have been taught in class, but sometimes the way math is taught emphasizes formulas at the expense of understanding.
1) Math is not about memorizing and applying formulas (unless you are a computer). It is about understanding why and how to solve problems.
2) If you understand the situation of the problem, you do not need the formula (although your teacher may require that you write it).
3)  is not the most effective way to calculate P(62,6).
SOLUTION TO THE PROBLEM:
Forgetting formulas, the first step is reading and interpreting the problem.
As you wrote it, the problem requires "different 6 character computer passwords".
I interpret that as meaning that AAAAAA, for example, is not allowed as a computer password.
If the 6 characters did not need to be different, we would have 62 choices for the first character, 62 choices for the second character, and so on, for a total of
 different passwords.
That can be rounded to the 5.6800325590x10^10 that you gave as one of your options.
However, the way I read the problem, all 6 characters in the password have to be different.
You have 62 ways to choose the first character, leaving 61 different characters
to choose the second character from, and so on.
The number you want to calculate is
(No memorized formula was needed).
Yes, that is the same as ,
and maybe your teacher likes to see that formula written in your homework and tests, but if you plug  into a calculator, you are first calculating
 and then you are dividing by  .
Why multiply times 56, 55, 54, 53, 52, and so on, if you are going to divide by the same numbers later.
That's a lot of doing and undoing the same operation and invites rounding errors.
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