License Plate Combinations

Date: 11/26/2002 at 09:52:06
From: Eric
Subject: Combinations

How many different combinations of license plates are there for our 
state, given that we have 6 spaces that can be (0-9) numbers and (a-z) 
letters?

I'm okay with one set of symbols, but with two sets of symbols what 
approach do I take?

Thank you.

Date: 11/26/2002 at 11:39:14
From: Doctor Ian
Subject: Re: Combinations

Hi Eric,

Try treating it as just one set of symbols, as if there were 36 digits
instead of only 10. 

This isn't such a weird notion. For example, computer programmers
often write numbers in base 16, also called 'hexadecimal'. Here's how
you count in 'hex':

   0  1  2  3  4  5  6  7  8  9  a  b  c  d  e  f
  10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f
  20 21 22 ...

So, if you have three spaces and you can use only numbers, there are 

  10 * 10 * 10 = 10^3

possible license plates.  If you can use only letters, there are

  26 * 26 * 26 = 26^3 

possible license plates.  If you can use either, there are

  (10+26)^3 = 36^3

possible license plates. 

Does this make sense? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 11/26/2002 at 12:48:52
From: Eric
Subject: Thank you (Combinations)

Yes, this helped out a great deal. Thanks again - you guys/gals are 
great.