How many passwords are possible?

Hi everybody,

I'm a bit confused about this one problem in my Barrons SAT II Math book. It reads, "A code consists of two letters of the alphabet followed by 5 digits. How many such codes are possible?"

Barrons gives the answer as (26)(26)(10)(10)(10)(10)(10)= 67,600,000 possible codes. I am confused because I think this method would produce repeat answers, and I think I would have to divide it by something, but I'm not sure what. (I"m not sure how to describe how I am confused, I just feel like this method would produce for example aa54865 twice and not take into account that aa is the same no matter what order the a's are placed in... Am I making sense?(Thinking)) Anyways, is Barrons right or am I? And if I am right, what would I need to divide by to get the right answer?

Thank you very much!

Re: How many passwords are possible?

26 ways for the first letter,

26 ways for the second letter,

10 ways each for the 5 digits

$26^2\cdot 10^5=67.6$ million codes. Barrons is correct. If you were just looking for a group of 2 letters and 5 digits where order didn't matter you would be correct but that's not the case here. Order matters in a code.

Re: How many passwords are possible?

Quote:

Originally Posted by

**precalc** I'm a bit confused about this one problem in my Barrons SAT II Math book. It reads, "A code consists of two letters of the alphabet followed by 5 digits. How many such codes are possible?"

Barrons gives the answer as (26)(26)(10)(10)(10)(10)(10)= 67,600,000 possible codes. I am confused because I think this method would produce repeat answers!

Why are you confused? Do you understand the multiplication rule?

You want to do two thing that can be done in twenty-six ways followed by an action that can be done in ten ways five times.

Re: How many passwords are possible?

Ohhh, I understand it now! Thank you very much Plato and romsek!